The Grand Mayan is a nice resort. I'll be going again next Feb/Mar. The resort does have it's own dive op -never dove with them, but I think they just go directly out from their beach - nothing very complicated and I can't imagine, IMO, there's much to see as I have done some diving at a few sites along this part of the coast.
Regarding Cozumel (based on my knowledge from a few years ago): The closest dive op is Dressel Divers located at the Iberostar Paraiso Beach Resort. They do pick up and drop off - you have to be out front of the Grand Mayan (as you would for any other excursion picking you up.) You could also walk along the beach to the Iberostar - about 15 minutes - but there are a couple of spots where the beach narrows mainly to iron shore and the water makes it a little slippery. I did a package with Dressel, to which I added a day to Cozumel. Once you get to their shop at the Iberostar Paraiso, they provide the transportation to Playa Del Carmen and back, the ferry ticket to Coz and back, transportation to their dive shop at Cozumel Iberostar (we were picked up at the ferry pier by a Dressel boat and taken to the Iberostar) and back to ferry, a day pass so we could eat/drink while we where there (which was about 15 minutes before going out on the dive boat and about 15 minutes after our dives), and of course 2 dives. We did the surface interval on the boat. The positives were that every aspect of the day was covered, someone was with us all along the way and everything progressed without any delays. The negative was that you had to carry your own gear all along the way - the drop off point in PDC was a longish walk to the ferry, likewise when getting back from Cozumel. You may have to book/pay ahead online. At one time, I had a WhatsApp number for the Dressel at Iberostar Paraiso, but can't find it - sorry.
There are other ops in PDC that do a day trip to Coz. I believe different ops have different ways of offering the Coz dives - most involve the ferry over and back (possibly with you taking care of that transportation) and a few have their speedboat going directly across - I know what the ferry is like going across and I've been on smaller speedboats in choppy water - not saying bigger is better but might be something to consider.
One other option I'll throw out. I have also caught a taxi out front of the Grand Mayan for a 10-15 minute ride to Puerto Morelos (toward Cancun.) There are some nice dive sites there. Of course the negative is the cost of a taxi.