First of all, stick with either 2D or 3D, do not mix them unless you have reason to. I am guessing you are doing a 2D game, so change all Vector3 to Vector2. Do not use volume checks (Bounding Sphere) in 2D worlds. Stick with rectangles, triangles and circles.

The 2DTexture is essentially a rectangle, so you can use it just as any other.

YourTexture.Contains(SomePoint) //Or YourTexture.Intersect(OtherRectangle)

Here are some additional ideas:
-I strongly recommend you to rename your Sprite class, the name is very confusing for someone reading your code.
-Do not show the score in the window title. Use a SpriteFont instead.
-You can use a list to keep all the game´s entities in and simply iterate trough the list every game update.

Good luck!

Bool isVisible=true; //start out so it IS visible

then, in your rendering code, change the third render call to:

if(isVisible) {spriteBatch.Draw(Sprite2.image, Sprite2.rect, null, Color.DarkSlateBlue, Sprite2.rotation, Sprite2.origin, SpriteEffects.None, 0);}

then it's simply a matter of setting isVisible to false when you detect a collision!

{ /// <summary> /// Alan Carstairs /// 26/9/14 /// </summary> public class Game1 : Microsoft.Xna.Framework.Game { GraphicsDeviceManager graphics; SpriteBatch spriteBatch; int DisplayWidth; int DisplayHeight; const float speed = 2.4f; //speed of image int PlayerScore = 0; // //structure for 2D graphics struct graphic2D { public Texture2D image; public Rectangle rect; } //structure for moving 2D graphics struct sprite2D { public Texture2D image; //Texture to hold the image public Vector3 position; //Position on screen public Rectangle rect; //Size & position public Vector2 origin; //Center point public float size; //Size ratio public float rotation;//Amount of rotation public Vector3 velocity; //Sprite speed and direction public float thrust; //Amount of thrust applied public BoundingSphere bsphere;//Bounding sphere //public int spriteNum = 1; //public int maxSpriteNum; //public bool alive; //public Enemy(Texture2D Texture, Vector3 position, Vector3 velocity, } sprite2D Sprite, Sprite2; graphic2D BackGround; Boolean GameOver; public Game1() { graphics = new GraphicsDeviceManager(this); Content.RootDirectory = "Content"; } /// <summary> /// Allows the game to perform any initialization it needs to before starting to run. /// This is where it can query for any required services and load any non-graphic /// related content. Calling base.Initialize will enumerate through any components /// and initialize them as well. /// </summary> protected override void Initialize() { // TODO: Add your initialization logic here DisplayWidth = graphics.GraphicsDevice.Viewport.Width; DisplayHeight = graphics.GraphicsDevice.Viewport.Height; base.Initialize(); } /// <summary> /// LoadContent will be called once per game and is the place to load /// all of your content. /// </summary> protected override void LoadContent() { // Create a new SpriteBatch, which can be used to draw textures. spriteBatch = new SpriteBatch(GraphicsDevice); //Load BackGround BackGround.image = Content.Load<Texture2D>("fullmoon"); // work out the ratio for image depending on screen size float ratio = ((float)DisplayWidth / BackGround.image.Width); BackGround.rect.Width = DisplayWidth; BackGround.rect.Height = (int)(BackGround.image.Height * ratio); BackGround.rect.X = 0; BackGround.rect.Y = (DisplayHeight - BackGround.rect.Height) / 2; //Sprite Sprite.image = Content.Load<Texture2D>("raptor"); //Sprite2 Sprite2.image = Content.Load<Texture2D>("raptor2"); reset(); // TODO: use this.Content to load your game content here } void reset() { //sprite // Set initial position Sprite.position = new Vector3(DisplayWidth / 2, DisplayHeight / 2, 0); Sprite.size = 0.2f; // set size of sprite Sprite.origin.X = Sprite.image.Width / 2; Sprite.origin.Y = Sprite.image.Height / 2; Sprite.rect.Width = (int)(Sprite.image.Width * Sprite.size); Sprite.rect.Height = (int)(Sprite.image.Height * Sprite.size); Sprite.rotation = 0;//speed of rotation //sprite2 // Set initial position Sprite2.position = new Vector3(DisplayWidth / 2, DisplayHeight / 4, 0); Sprite2.size = 0.2f; // set size of sprite Sprite2.origin.X = Sprite2.image.Width / 2; Sprite2.origin.Y = Sprite2.image.Height / 2; Sprite2.rect.Width = (int)(Sprite2.image.Width * Sprite2.size); Sprite2.rect.Height = (int)(Sprite2.image.Height * Sprite2.size); Sprite2.rotation = 0;//speed of rotation GameOver = false; } /// <summary> /// UnloadContent will be called once per game and is the place to unload /// all content. /// </summary> protected override void UnloadContent() { // TODO: Unload any non ContentManager content here } /// <summary> /// Allows the game to run logic such as updating the world, /// checking for collisions, gathering input, and playing audio. /// </summary> /// <param name="gameTime">Provides a snapshot of timing values.</param> protected override void Update(GameTime gameTime) { GamePadState pad_P1 = GamePad.GetState(PlayerIndex.One);//reads gamepad 1 KeyboardState keys = Keyboard.GetState(); // reads keyboard // Allows the game to exit if (GamePad.GetState(PlayerIndex.One).Buttons.Back == ButtonState.Pressed) this.Exit(); if (!GameOver) { //collision detection if (Sprite.bsphere.Intersects(Sprite2.bsphere)) { Sprite.image = null; PlayerScore++;// increase Points } //Display score in top lefthand side of the screen this.Window.Title = "Score: " + PlayerScore.ToString(); //sprite Sprite.thrust = (speed * (pad_P1.Triggers.Right + 2));// calculate the amount of thrust based on speen and right trigger Sprite.velocity.X = pad_P1.ThumbSticks.Right.X; Sprite.velocity.Y = -pad_P1.ThumbSticks.Right.Y; Sprite.velocity *= Sprite.thrust;//multi velocity from the thumb stick Sprite.position += Sprite.velocity; //add current velocity to pos of thr // check if ball hits any of the four sides and bounce it off them if ((Sprite.position.X + Sprite.rect.Width / 2) >= DisplayWidth) //RHS Sprite.position.X = DisplayWidth - (Sprite.rect.Width / 2); if ((Sprite.position.X - Sprite.rect.Width / 2) <= 0)//LHS Sprite.position.X = (Sprite.rect.Width / 2); if ((Sprite.position.Y + Sprite.rect.Height / 2) >= DisplayHeight) //bottom Sprite.position.Y = DisplayHeight - (Sprite.rect.Height / 2); if ((Sprite.position.Y - Sprite.rect.Height / 2) <= 0) //Top Sprite.position.Y = (Sprite.rect.Height / 2); // set position of Sprite into the rectangle from the position property Sprite.rect.X = (int)Sprite.position.X; Sprite.rect.Y = (int)Sprite.position.Y; //set bounding sphere Sprite.bsphere = new BoundingSphere(Sprite.position, Sprite.rect.Width / 2); //sprite2 Sprite2.thrust = speed * (pad_P1.Triggers.Left + 2);// calculate the amount of thrust based on speen and right trigger Sprite2.velocity.X = pad_P1.ThumbSticks.Left.X; Sprite2.velocity.Y = -pad_P1.ThumbSticks.Left.Y; Sprite2.velocity *= Sprite2.thrust;//multi velocity from the thumb stick Sprite2.position += Sprite2.velocity; //add current velocity to pos of thr // check if ball hits any of the four sides and bounce it off them if ((Sprite2.position.X + Sprite2.rect.Width / 2) >= DisplayWidth) //RHS Sprite2.position.X = DisplayWidth - (Sprite2.rect.Width / 2); if ((Sprite2.position.X - Sprite2.rect.Width / 2) <= 0)//LHS Sprite2.position.X = (Sprite2.rect.Width / 2); if ((Sprite2.position.Y + Sprite2.rect.Height / 2) >= DisplayHeight) //bottom Sprite2.position.Y = DisplayHeight - (Sprite2.rect.Height / 2); if ((Sprite2.position.Y - Sprite2.rect.Height / 2) <= 0) //Top Sprite2.position.Y = (Sprite2.rect.Height / 2); // set position of Sprite into the rectangle from the position property Sprite2.rect.X = (int)Sprite2.position.X; Sprite2.rect.Y = (int)Sprite2.position.Y; //set bounding sphere Sprite2.bsphere = new BoundingSphere(Sprite2.position, Sprite2.rect.Width / 2); // user presses X game is over if (pad_P1.Buttons.X == ButtonState.Pressed) GameOver = true; } else { if (pad_P1.Buttons.Start == ButtonState.Pressed || keys.IsKeyDown(Keys.Enter)) reset(); } // TODO: Add your update logic here base.Update(gameTime); } /// <summary> /// This is called when the game should draw itself. /// </summary> /// <param name="gameTime">Provides a snapshot of timing values.</param> protected override void Draw(GameTime gameTime) { GraphicsDevice.Clear(Color.CornflowerBlue); // TODO: Add your drawing code here //Draw ship spriteBatch.Begin(); spriteBatch.Draw(BackGround.image, BackGround.rect, Color.White); //sprite spriteBatch.Draw(Sprite.image, Sprite.rect, null, Color.DarkSeaGreen, Sprite.rotation, Sprite.origin, SpriteEffects.None, 0); //sprite2 spriteBatch.Draw(Sprite2.image, Sprite2.rect, null, Color.DarkSlateBlue, Sprite2.rotation, Sprite2.origin, SpriteEffects.None, 0); spriteBatch.End(); base.Draw(gameTime); } } }