simplest things first:
1) make sure you have the "RevTech" feature on the ignition sw. panel prooerly engaged. Then attempt to operate the tractor as you have described.
The reason for this is your forward /reverse drive pedal is a relatively sensitive single "rocker" pedal - and you my be unwittingly momentarily tipping it toward reverse which will immediately shut down the deck. Having the RevTech feature engaged will eliminate this from happening.
2) if prob still exists, remove batt, take to qualified shop and have it Load tested. A marginal battery can sometimes cause intermittent PTO problems.
3) Beyond that, suggest getting qualified shop help. The related control circuitry is somewhat complex and is best diagnosed/repaired by qualified personnel.. mho. Good luck.

If your mower has the mow in reverse feature, engage that and see if the problem continues. It is common on these that the harness for the reverse switch (in behind the Right rear wheel breaks and then the tractor thinks it is in reverse when the wire shorts itself.

By, "...the mower switch stops the mower from turning...", do you mean than you switch-on the mower, and the engine bogs-down and stops? Or is it more like simply shutting-down the tractor?

If the former, then maybe the engine is cold and you need to use a little more choke until it warms-up.

If the latter, then I concur with the other suggestions.