Another trick is to line the pan with foil or parchment paper, in both directions, so you can simply lift the baked brownies out in one piece before you cut them.
Lift them out of the pan, put them on a cutting board, and use a long knife to cut them.
(I can’t decide if they cut more neatly when warm or totally cold. Anyone else have more definitive experience? My results seem inconclusive, but then again, I seldom use the same recipe twice in a row.)
Another idea entirely that makes for easy, neat service, is to put dabs of brownie batter into mini-cupcake/tartlet tins. Don’t overfill them with batter, and don’t over bake. I find it easier to load the cups if I put the batter into a plastic bag and snip off one corner and use it like a pastry bag. HTH!