TEB Tower Controller reported problems with seeing the end of a runway due to trees and almost had a runway incursion due to the trees and not being able to see aircraft on the runway.

Narrative

I cleared Aircraft Y to land about 10 miles out. I had Aircraft X in position waiting for another aircraft to roll out on Runway 6. Once Runway 1 was clear of the arrival from Runway 6; I cleared Aircraft X for takeoff. Aircraft Y was on a 2.5 mile final for Runway 6 at this point. I did a few other things then Aircraft Y asked if he was OK to land Runway 6 at short final. I said affirmative and started looking for Aircraft X because he should have well been airborne. I couldn't find him out the window and realized he just began his departure roll once he cleared an area where trees block the view of the approach of Runway 1. I tried canceling Aircraft X's takeoff clearance and he did not do that. I sent Aircraft Y around with an immediate heading of 360. I then tried turning Aircraft X to a 90 [degree] heading and he did not turn. I then told Aircraft X to go to the Tower; which he did. That would have put him at an approximate heading of 060. Since Aircraft Y turned immediately; he was far enough away from Aircraft X and everything worked out. Trees block the line of sight approach for Runway 1. I could not see Aircraft X. I reported last year [previously] that trees were an issue. Port Authority tried to cut trees but did not cut the right ones. Aircraft X may need a better radio or listen better.