If one has a disadvantage meaning that he gains a tail (strange appearance disadvantage). Now he can try to hide it no problem. But if he wants to make sure that its hidden he would have to cut it off. So th equestion is, does this count as taking a wound?
Yes, this would cause a wound. We can triangulate on this conclusion by looking at the rules for injury and the rules for this particular flaw.
Consulting Injury and Death (p. 95), it definitely is worse than the “minor aches and scratches” that Stamina represents at worst, and would count as requiring “extended rest to recover”, and “require the attention of a skilled medic or doctor” to avoid infection and ensure full healing. The pain and blood loss would also affect the “fundamental survivability of your Hero.”
Strange Appearance (p. 22) is a flaw that is worth +0 if it's “easily concealed”, so if cutting off the tail doesn't cause injury, then it's a +0 flaw (and I have to wonder why the character's creator bothered taking it). It's also safe to say that cutting off a piece of your own body is not what “easily concealed” means, so it should have a consequence greater than mere Stamina loss.
(But more importantly, don't take a flaw that you don't want.)