OK, time for some math homework. 60 x 120 area = 7200 square feet, times 9 feet deep, = 64,800 cubic feet, if it had straight up and down sides. Which it won't. Recommended slope in a Florida pond is 3:1. If your pond is a perfect square (which it won't be), The only part that would be 9 feet deep would be a strip 6' wide by 66' long. The rest of it will be an average of 4.5' deep. The corners will be curved, which will reduce the actual amount of dirt to be removed, but let's stay with the swuare corners and over-estimate it just to be safe (and because it's easier).
So, let's refigure the amount of dirt. The deepest part will be 6' x 66' x 9', or 3564 cu ft. The sloped sides will be 27' x 120' x 2 (for the 2 long sides) + 27' x 6' x 2 (for the 2 ends), 0r 6804 sq ft, x 4.5' average depth, which is 30618 cu ft. Adding them together, the total cubic feet is 3564 + 30618, or 34182.
Now, to convert to cubic yards, divide by 27. The total cubic yards are 1266.
As I said, that would be for square corners - a little less for round courners, a little less for an inrregular shape. In fact, if it was a really irregular, there would be very little of it that would reach the depth of 9'.
You can cut down on the yardage a little by going with less slope (flatter) above the water line, which will also make it easier to mow. My contractor is going with 5:1 above the water line, 3:1 below it. However, the flatter the slope, the less chance you have to reach the depth.
Remember that your water table is going to vary. It may not vary as much up where you are, but down here in Okeechobee, our water level a couple of days ago varied from zero to -2" (this is on my son-in-law's improved property next door, where portions of his 2-1/2 acres were ankle deep after several repreated rain storms; I have some deeper spots, but I don't have my pond and drainage in yet). His pond was about 1'. In the dry season, that will be 6' to 8' lower. Down here, at 9' from the surface, your pond would be a mud hole part of the year. I'm planning about the same thing, maybe a little wider (80-85') in order to get to the depth, but I plan to have the water level held constant by pumping from the well in the dry season.