dherik 
A little card board and wood fire. Then some times the metal pieces will just fall off easy or a few hits with a hammer , I seen all sorts of transformers , Each has it's own weakness to get at the copper. The fire burns off the paper or bit of the plastic.Transformers in general don't smoke as bad as wires.But still probably not legal . As I have seen town laws stating burning metal by it self is consider not legal
If it was like a micro wave trans you will have an easy time but yours looks like the harder type. Start by removing those screws then see if metal has any spot welds that can be popped off
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