From looking at the code I'd say the problem may be in line 76:

1.   for (int i=1; i<blocks.size(); i++) {

ArrayLists start at 0 (zero), so you're not removing everything. A shorter way to clear everything is to use:

1.  blocks.clear();

Also you may want to look into generics to prevent typecasting.

I wanted to keep block 0, because it is present in every level. The program is actually removing them, because if I print the size of the arrayList it gives me 0. The problem is that the blocks for some reason stay on the screen. I tried adding the clear() function, but the problem persists.

When I test it starting with int level=0; and these levels...

1.   case 0:
2.     blocks.add(new Block(2, 0, 0));
3.     break;
4.   case 1:
5.     player.xpos=1;
6.     blocks.add(new Block(3, 2, 5));
7.     break;
8.   case 2:
9.     player.xpos=0;
10.     blocks.add(new Block(4, 0, 0));
11.     break;

It shows very clearly that all previous level blocks are cleared. So I don't understand what do you mean by "stay on screen".

What I mean is the blocks from the previous level aren't removed. Instead they continue to be drawn where they were when the level was ended, except you can't move them.

Put your size() call at the start of setup().
And the loop

1.   for (int i=1; i<blocks.size(); i++) {
2.     blocks.remove(i);
3.   }

isn't correct, because the size of the list changes when you remove stuff in it.
One way to do this is to start at the end of the list.
Another way is even simpler:

1. Block b = blocks.get(0); // Works if you declare ArrayList<Block> blocks = new ArrayList<Block>();
2. blocks.clear();
3. blocks.add(b);

Thanks, that worked. It kept showing the blocks, but I realized that it was just because of the way I coded it. Instead of having actual blocks, it recolors a grid, and the grid wasn't resetting to the default grey.