Samsung Galaxy Note 3 : Tried to install TWRP, can't boot into recovery mode now
I had the same problem like you before. But I figured out the solution. We both downloaded and flashed the wrong TWRP version for Note 3 N9005: ha3g.img.tar. The correct one is hlte.img.tar which you can download on this link: https://dl.twrp.me/hlte/ 

I hope it helps you :)