I'm not familiar with woods of the South or NE, but some woods in the NW are best carved green; for example, alder is too hard & brittle to carve otherwise. Professional carvers from my tribe will even harvest alder, debark it, split it, and store roughed chunks in water for future use.

The only trees I will actively cut are alders, which fill in roads & trails if left unchecked. Otherwise I look for good wood that's already died naturally, my favorite being western red cedar. The stuff never rots.

Happy whittling! Leaving behind wood chips is worlds away from leaving stone chips. I wouldn't worry about it.