Billy Bob, even without knowing the size of the glass,I would strongly suggest that you use a thicker glass than 2mm. The actual thickness of 2mm usually varies between 1.5-1.8mm. You did not say whether or not this is to remain a functional cabinet door. As opposed to a cabinet door that will now hang on the wall as an piece of art.
Assuming it's the former, imagine what would happen if a child or worse, a teenager slams that door shut.
As a glass fabricator, we also sell glazing materials to furniture and cabinet makers. The thinnest substrate typically used is 3mm(1/8").
Depending on the application, it may need to be thicker, such as 3/16(5mm),1/4(6mm,)or even tempered.
With respect to seaming the edge, all the suggestions regarding different abrasives would work fine.
JohnR's post is 100% on the mark.