Yes sort of, the detonator will not set off mines only C4 charges but you can explode a C4 charge which will cause the mine to detonate as well if the C4s blast range hits the explosive.
Thanks, thats exactly what i wanted to know, which is why i said "C4" and not "Detonater" on a side note, What about Missiles?
No. the only way to detonate missiles is to fire them from a missile launcher.
You can set off mines with any explosion (a fire extinguisher will do it) or even by shooting them with regular bullets, or anything, really. This is if they're active (have been placed, and the little light goes on); if they're just on a shelf or otherwise stored they'll just get tossed around by an explosion.