You can shoot the mines: first tip is to use Long Range Scan; this may show up a bunch of '?' spots that you can select on HUD radar (doesn't always happen, & the markers aren't necessarily persistent (maybe they''ll show up better from long range?; haven't tested as yet). SRS appears to be useless for mine detection currently.
According to others, yellow mines are FoF, blue are <something> (I forget - poss track mk 1?) & red are tracking, so yellow mines are the least threat. Either way, for this particular mission type you're only likely to have a patience problem: the other two are targetable (IME). Check mine blast (AoE) radius in the encyclopaedia, likewise track range. It may be currently inacurrate but it'll at least give you an idea. I've had no problems with yellow mines at approx 1-2km range, blues at 2-3km & red trackers at 3-4km. Bear in mind that several mines may be set off if you hit a group, so try to alternate shots between closest to <target> & far away, to allow <target's'> shield to recover - <screenshots needed>
Tip 2: if you fly close enough (in your ship ofc, not the suit!) to the mines you may see a tiny grey dot at the centre of the glow: this is what you shoot at. Don't get too close! :)
Tip 3: You can try 'spray & pray' tactics from a minimal distance, but that frequently doesn't help much. However, if you're within shooting range of the mine(s) you can use /very careful/ /tiny/ aim adjustments to identify where the 'hit dot' will land. It takes patience & skill, but the gimbal tracker will eventually lock on to a valid target (ie mine) rather than bouncing around, even if it's only 1 out of however many guns you have <ideally a short vid clip here, but maybe a screenshot will suffice>
Tip 4: for those 'recover ship' missions you don't need to destroy all mines, only those required for you to board the ship & fly it out of the 'field & back to its station safely. IMO it's best if you clean up the junk completely tho :)
IME the 'retrieve ship' missions (when you have to dock the pilotless, mine-surrounded ship back at a station) tend to spawn these 'untargetable' mines: expect to see several more of these missions appearing as you do (at least) the Teladi trade mission chain (unless it's patched out ofc :) )