I managed to solve this myself but thanks to masijade for his help.
What you have to do is delete the value from the binary search tree and then update the tree.
Here's the code that I have which is attached to a "Delete" button on my GUI:
JButton delete = new JButton("Delete");
public void actionPerformed(ActionEvent e)
deleteIt(checkTree()); // Get item to be deleted
Shapes widget; // Update the BST with the info
widget = new Shapes();
myFrame is actually the name of the frame for my GUI. The shapes class draws all the shapes that I need.
Hope this helps anyone that needs it. If you need more help send me a message :P