Well it might push them out for a bit but they will be back. Especially since the pre rut is looming right around the corner..

I know everyone tries to be quiet as possible but I hung a new tree stand today for November (last min. decision?).. Well anyway, I try to make some noise so the deer don't come in and spook when they see me hanging 20ft. off the side of a tree.. lol Farm noises are the norm around me though so I suspect after a few days they will be back just fine.
Deer are very skiddish though, probably depends on what they are used to.

Only way I would be quiet as possible is if you knew when that deer was in the area. Go in when you know he's not there and make it a quick and quiet trip. No matter if it's during mid day or mid night..

As far as trees go.. I dont think it will matter too much as long as your not clearing the forest. I few young trees that are in your shooting lane will probably not matter much. Deer (in my area anyway) are used to seeing things move around, trees fall and just naturally branches, walnuts etc falling constantly..

So in my humble opinion.. Cut away but do it soon and leave it go for a couple weeks before returning. I have heard of it screwing with deer patterns but I'm just speaking in general. And like I mentioned once the chasing begins it won't matter at all..