10-15 mins depending on the size of the field
Do you have any idea how long that actually is in game? I REALLY don't think it takes that long. I'd say it'll take from 45-90 seconds if you fly your flak frigates and scouts in a fleet formation straight through a minefield at a decent pace. Flaks are great at taking down mines, especially since they can take a couple hits from some and keep chugging along, a single one can target 4 at a time (eventhough 1 will take a couple of rounds of fire to destroy 1 mine, 3-4 will blow-em up pretty quick.) Plus if a couple of mines end up blowing up on your fleet, what did you lose? a couple of scouts and flaks? Big woop. Also if you enter a well where mines are still being placed, the flaks can destroy the mine layers (ruiners/contruction vehicles), or protect your scouts from fighters (drone hosts). Lets see Ogrovs do THAT! Given the choice, I'd pick using flak frigates for clearing mines over SC simply because A) Unless you set the fighters to hold position and move them with the scouts, flaks will take down the mines faster and Flaks have a longer range than fighters do, so If you were going to set your fighters to hold position to take down mines, you may as well just use flaks.
As far as Homing mines are concerned, I believe the scouts detection radius and homing mines detection radius are almost the same, making it difficult to destroy them with just scouts alone. The homing ability works as a double edged sword, while its makes it the field MUCH more dangerous to fleets, you will lose more to enemy ships just passing through than the stationary vasari and TEC mines.