I had a similiar problem, but going across a hill. Gas tank was full at the time, mowing off about an inch of new grass.
I suspect a carb adjustment is in order, with a 'shot' of carb cleaner or sea-foam.
Welcome to MTF, peanut.
I recently had a similar problem, and found a solution (well, at least it worked for me). It turns out that the gas cap vent was the issue, or the lack of venting to be more to the point. Somehow the vent in the cap stopped working. When I removed the cap, there was a huge inrush of air. Ah HA! So I put the cap back on loosely, so as to keep dirt/etc out and the gas in, but to permit "venting". Mowed the entire lawn (hilly, 4 acres, dips, trees, etc) without incident. Problem solved, now have to order a $10 gas cap as they don't stock it locally.
Oh, and I'm running a 2007 DGS6500 26hp Kohler 54" deck.
Same problem here last weekend. Half way up an incline, the tractor starts to sputter and slows to almost a stop. Unscrewed the gas cap, tractor went back to normal.
I thought that was the last I'd hear of it. BUT, it did it again, going up hill. Unscrewing the cap didn't solve the problem this time. Upon further investigation, discovered that the carb feed from the fuel tank was dry, even thought there was 1/4 inch of fuel left. It has a small ridge around the feed, I suppose, to trap crap from going to the engine.
Note to self: Fill the tank next time. Then check the oil.