Can I carve up a suckling pig like you would an adult pig?
A suckling pig would have the same cuts as an adult, but they would obviously be much smaller and thus fiddlier to butcher. 

Wikipedia reports that suckling pig meat is also quite gelatinous, so you might take all the time to butcher the thing and end up with meat you don't want to eat.

You could always start with half a pig, since they are obviously symmetrical, joint it up and then freeze and/or give away the various cuts. Cuts like the belly could be cured, and other cuts could be ground/minced or turned into sausage.