Remove paint from concrete floor (indoors)
For mechanical removal of paint from floors....

If you're talking about drips/splatters/spills that are on the floor from painting the walls/ceiling you can use wire or bristle disks that are meant for removing paint/rust and there's also the Wagner Paint Eater.

If you're talking about the whole floor covered in paint you can rent a floor sander with an abrasive diamond pad or a shot blaster. 

All of them are messy and generate a lot of dust. Shot blaster also removes any weak/soft concrete at the surface which could improve your tile adhesion.