funny, I tried that in my ASP, but never ever got an interdictor to fly into the mines, so after ten interdictions (one of it lethal), I switched back to lasers
I found, when I started using mines was that while I was lining up my targets directly behind me I was not paying attention to their difference in Z-axis. If they are flying (behind and) above or below your own flight path, you must maneuver so that your intended target is
both directly behind
and exactly level with your own vessel, or when you drop your mines the target will fly right over or under them. You also need to designate your target before dropping the mines. I am not sure if that step is mandatory but it seems logical. When dropping mines, don't skimp on the mines! Sometimes they will do ALL the work for you! Also, do not drop a couple of mines and wait to see what they will do, the feedback delay is too long and you will never get his shields down. Drop 8 or 10.
Short checklist for defeating NPC interdictions using mines:
When interdicted, immediately submit. Saves time (I'm working on a deadline) and shortens FSD cool-down time.
Set pips to ENG, boost once (gains some distance, decreases chance of direct attack), designate target, deploy hard-points.
Line up your target directly behind
and level with your own vessel.
Drop 8-10 mines as fast as you can (2 less for Sidewinders, etc., 4 more for Annies, FDLs, etc., your mileage may vary). Boost again to stay out of his WEPS range.
Monitor the depletion of your target's shields. When they drop the NPC may try to run away to recharge them. If you do not chase him down and destroy him he will just come back, so:
Set pips to WEPS, turn into him and burn him down with multi-cannon and laser fire. Scan destroyed ship debris for interesting/valuable cargo.
Leave, quickly before the cops show up and blunder into one of your mines, putting you on a bounty.
Open your transactions tab and smile reading your list of un-collected bounties.
EDIT: If you drop a bunch of mines and he flies right by them it is probably a good idea to boost, spool up the FSD and fly away to figure out what went wrong rather than try and fight it out. Just saying . . .