I have worked on a lot of Snapper walk behind mowers, but I am unfamiliar with any ones that have (2) friction drive wheels.
Does this mower have a power reverse?
On most of the units I have ever worked on the driven disc is operated by a belt from the crankshaft of the engine and then the rubber friction disc is driven off of the driven disc.
Both the drive belt and the drive disc are tensioned by springs, if either one breaks or comes off then the transmission will slip.
If you can find a model number off your unit, that might help with figuring out what kind of set up you have.