Doubt there is much from the beach, try the Jungle Tour speed boat trip. It is throughout the lagoon/inner harbor and ends at the outlet where they let you snorkel. Within seconds I had a huge ray just below me
We stayed at Dreams Cancun a few years ago, and while we were there we hired a boat to take us a little ways out (I think to the reef?). It was maybe a mile out from the resort, because we could still see land. We spent an hour out there and saw sea turtles, lots of rays, and lots of colorful fish. Not sure if you could do something like that at TTR, but we'd like to try.
Boobs Cruise has gear along that they hand out and we stopped for 45 mins or so...I didn't do it, but the people on the last one I was on were happy enough with the location. I'd think if you wanted more than that, you'd want to sign up for a specific excursion. I know there are several that highlight it.
The speed boat tour was fun and the snorkeling was good. Losts of fish and the tour is a few hours long.
We did the speedboats right next door (I think it's called Jungle Tour) and it was pretty good, about 2 to 3 hours. We are thinking about doing it again in April because those little speed boats are a blast.