well if you been mowing them on a regular bais , I say you can mow as late as you want, as, by now deer should be conditioned to you doing so, and not take it as a threat
deer get used to being disturbed if it happens over and over from spring till now
and don't forget , deer prefer to eat new growth , after a cut, so cutting your actually making the food more attractive to them, and they should know this if you mowed a bunch of times
Mowing here actually will attract more deer a day after or so after I mow!