MPS's treecapitation works on natura redwoods. I think TC axes should work just as well, though it would only cut as much as its dur would allow.
Edit: Yea, using the lumber axes on a redwood tree makes it act like it's mining similar to the hammer.
Yeah, I figured that, as they don't pick up the robust Twilight Oak as a tree (I think because it lacks leaves within 30 blocks) that the redwood would probably be similar.
Given that Natura is a compliment to TC, it's possible that it's deliberate, otherwise someone would be carving out a new room in their treehouse only to discover that the roof disappeared.