In the game, use hotkey V to open the ships database, then tag the Mines button. You'll find that 'Mk 10 Mine' has a load cost of 630.
The manual 220.127.116.11 shows that you'll need a size 6 Port (rearm level 700), assuming no Naval Support. Manual 18.104.22.168 says that the port rearm level is increased by 5 for each undamaged Naval Support Device present. I've checked 2 ports in my game, & the port screen's Re-arm level includes the Naval Support effect. (Brisbane size 7 = 5500, plus 5 x 100 NavSupp, displayed Re-arm level is 6000) (Pearl Harbor size 8 is 6000, plus 5 x 552 NavSupp, displayed Re-arm level is 8760).
Open the game's Intelligence screen (hotkey I), tag 'All Device types' to turn everything off, then tag 'Mine' to show mines. Check that you have enough Mk 10 Mines available 'In Pool' to provide a full load for all subs in the TF, & that 'Stockpiled' is set to N.
It's possible that the scenario you're playing has been altered by its designer to exclude these mines, perhaps because there was no historical use of them during the campaign.