Dogs < Cats

my sisters dog every morning at around 5am starts barking for no reason, then pokes its nose at the gate until it opens a big enough gap to fit through, then goes over to this tree and shits on it, then goes back and continues barking.

I eventually got sick of getting woken up by this, so i went out the other night and ripped its bottom jaw off with some nifty clamps and a saw i found in the shed. But it still can bark and get through the gate.

What should I do next?

I dunno but do something quick or you will get trauma and want to kill it later...