Something to consider:
A faction's resources determines the quality of the stuff the squads get outfitted with. With high resources, they get exo suits and sniper rifles. With low, simple jackets and pistols/smg's. As you can imagine, a faction with low resources will have a VERY hard time beating a faction with high resources.
It's like this: When a squad dies, a new squad is then created. The new squad dips into their factions resources by equipping themselves with whatever is in their arsenal. This causes a loss of resources. As more and more squads are killed, the enemies resources are depleted by constantly giving out replacement gear to the new squads. Eventually if there arsenal has been cleaned out of all the good stuff, they can only give the new squads crappy equipment, which is when the faction resources are practically at zero.
Factions get resources by taking and holding territory. If they own everything, resources are easy to get. If all they have is their headquarters, it will be like using a depleted vespene geyser from starcraft. So if an enemy faction loses all it's territory AND is having it's squads wiped out constantly, that will be the fast track to their faction becoming totally crippled.
Although you cannot truly remove a faction from the game since they can always spawn a few squads inside their HQ when you aren't around, it IS possible to put it on lock down so they can never branch out! It's easy:
1. As mentioned above, get the enemy faction to have as low resources as possible so they are stuck using pea shooters and crappy jackets.
2. Wait until your faction has almost full resources so the squads are carrying the best gear.
3. Go to the enemy base and do your thing: but DO NOT LEAVE IT! Enemy squads will not respawn if you are close to their HQ.
4. If you have the patience, wait around for a bit inside the enemy HQ until 2-3 of your faction's heavily equipped squads arrive to secure the place.
With those exo suit wearing squad members armed with snipers/HMG's sitting inside the enemy base, any squads that spawn inside will get wiped out by them about 90% of the time, never being able to retake their own base thanks to their inferior gear! By doing this, you will never have to worry about that faction again...Unless you go rogue and start murdering your own guys.