Popular Pro 625 series. starts and runs but why does it die while cutting?

SOURCE: Mower won't start

13 to 15 amps electric or battery operated mower may runs slow when cutting thick grass. also recommended not to cut grass when it's wet & need very sharp blade to do the lawn. may overloading it, cutting grass too thick also draws too much power. check house breaker first.

SOURCE: riding mower

If the grass is very tall (more than 10") you will have to slow down to less than 1 mph, if you have a mulch kit on this unit, remove it to get the grass out as quickly as possible. Also, sharp blades & a level deck are important.

SOURCE: Airens Zoom 1944 ZTR Blades Slow Down In Bahaia Grass

You mention many PM issues but do not mention a blade sharpening. I don't get on my ZTR without a freshly honed blade installed. "That's" what cuts bahia grass...the blade. You can put all the horsepower you want behind the lade but if you're trying to cut grass with a 2X4 it rips more than cuts grass.

SOURCE: i have a craftsman gt 5000 model 917.276220 runs

not possitive, but sounds like 1 of the bearings on the mower deck is starting to seaze up.I would start with that. Remove the deck and belts and check all the pullys and bearings for free movement.

SOURCE: john deere 420 has loud pop and motor quits

take off the valve cover and see if the valves are opening