Grout lines are indeed easier to drill through than tile. And errant drilled holes through grout are easier to repair should the need ever arise.

It's still best to hit a stud if you can. I'll try for two fasteners through the wall to hang the mirror from. If you can't find the studs then use an appropriate wall anchor.

Very seldom do I hang the mirror off of the D-hooks though. I'll either run a wire from D-hook to D-hook, or remove the D-hooks and run a wire from frame to frame, then hang the mirror off of the wire.

Then there is the french cleat. Home made or commercially manufactured.

With large mirrors, sometimes a version of the french cleat is easiest, but that can depend on the mirror frame. As shown in the photos above, you can make your own french cleat, or buy them at the box stores.

Good luck with your project!