I suppose you could make the first question on the ballot something like "Do you give a shit?"
With electronic voting machines, anyone who answers "No" could be immediately given a receipt without seeing a single ballot option. If these people already don't care at all, why are they going to want to spend time going through a list of candidates for president, senate, house, local senate, local house, elected judges, water reclamation district, non-binding ballot questions, etc. They will say no and GTFO.
Of course I still can't get behind mandatory voting. You should be free not to, and still having to show up and check the "No" box is not a valid substitute. Make it a holiday (not on a monday or friday, as people will just turn them into long weekends and not even be in town for voting); some people still have to work on holidays, but it takes a lot of the pressure off. Or figure out how to do it from home without fraud (Estonia figured this out...and we already do it from home if you count mail-in ballots). Otherwise you will just have a bunch of uninformed idiots voting. Maybe you will get lucky and they will all vote for joke candidates...or maybe they will all vote for the guy who runs on the platform of "Lets end mandatory voting".