youYou can use command blocks. placePlace a redstone torch under the block you want to break and a command block above. thenThen, the command is:
/setblock <x> <y> <z> minecraft:air 0 destroy
in your case it will be:
/setblock 0 0~ ~-1 ~ minecraft:air 0 destroy
otherOther than that, there is no vanilla way. (this is also not very vanilla)
toTo pick it up by a hopper place the torcetorch on a wall under it and place the hopper at least 2 blocks under the cobble to make shuresure that you don't power the hopper