There are green reptiles, insects, fishes, amphibians but no green mammals.

What's the for this?

Weeeeel…..The sloth is sometimes green because of its a symbiotic relationship with green algae that inhabit its fur/hair – whatever it is. It presumably adds a touch of camouflage, which added to the lack of movement that sloths generally indulge in means that it's more difficult to see and therefore to kill.