I've played with this quite a bit on my CNC machine, needless to say it's been quite a learning process.
Here's the factors you're working with:
Imagine your object just laying on a table, it is fully surrounded by air. Assuming you're somewhere near sea level, all the air surrounding the object is at atmospheric pressure at 14.7 pounds per square inch. Unless the object is sealed to the table, atmospheric pressure is pushing equally all around the object.
With vacuum hold down, what you're trying to do is to remove as much air as possible that is underneath the object. If you can remove all the air that is between the object and your vacuum holding fixture, the air above the object will push the item down on the fixture at 14.7 pounds per square inch.
You can add all the "suction" you want, but once you are able to remove the air beneath the object, you will never hold it down more than 14.7 pounds per square inch. If I did the math right, your 1.5" dia. disc would have a max of 26# of atmospheric weight holding it down.
Conversely, if there is a lot of air leakage between the fixture and the disc, you'll never remove enough air between the disc and the table to have the full weight of atmospheric pressure bearing down on it. For small objects, a moderate size shop vac will supply more than sufficient air flow. Venturi units are better than vacuums for prolonged running (with a sufficient sized air compressor) but the trade off is the amount of airflow.
Either way you need a good gasket between the fixture and the object.
The other important thing is the amount friction between the fixture and the disc. The more contact area between the fixture and the disc and the "grabbier" the contact area is, the less chance of the disc sliding off the fixture.
With a little ingenuity and experimentation, you can build a simple vacuum hold-down fixture out of abs plastic. You should be able to purchase online an abs flange like you would use to hook your vacuum hose to a piece of machinery. Buy a scrap of abs sheet stock the same dimensions as the flange (preferably smooth both sides), drill a 3/8" diameter hole through the middle of it and glue it to the flat side of the vacuum hose flange. Make sure there aren't any gaps in the glue. If you're using a vacuum pump or a venturi unit, you can make a fixture out of 3 layers of abs glued together with the middle layer being used to create an internal passages from an air fitting on the edge of the glue-up to a center hole.
Source a small piece of 1/16" thick closed cell foam gasket material, preferably with adhesive on one side. http://allstaradhesives.com/
Here's where the experimentation starts. You need a slightly larger than 1-1/2" diameter ring of gasket material, maybe 1/4" wide, centered on the hole to seal around the perimeter of the disc. You might need more contact area with the gasket material to provide friction to keep your object from sliding. So you can fill in some of the space inside the 1-1/2" diameter ring with more pieces of gasket material, leaving little channels between the pieces to facilitate the removal of air between the disc and the fixture. Maybe you'll need to enlarge the 3/8" diameter hole.
If you are only polishing one side of your disc, sometimes it helps to leave the paper on the other side for more friction, sometimes it doesn't because the gasket material could possibly create a better seal with a smooth plastic surface. If you are polishing both sides, be aware the often the final polishing compound has silicone in it which can make your disc really slippery.

Some experimentation should bring you to a combination that works.
Good luck.
Al Waddell