How to make a piston turn a block into an item on Minecraft for PS4?

If your playing on 1.14 i do believe that TnT duplicators aren't patched yet. So you can use it to break the blocks as TnT now drops all blocks it breaks. Place a collection at the bottom (Coat it in obsidian). If you don't know how to make a TnT duplicator, I think youtuber Mumbo Jumbo has a tutorial on how to do it. If not you should be able to find one by someone else. Hope this helps!

There is no way to break cobble automatically using only redstone and pistons. You can, however, use tnt, creepers, and withers to destroy the blocks.