My cat's food bag is filled with ants and I'm sure I'm not supposed to give him ant filled food. So is there a method to remove the ants from the original bag or should I throw it away and get a new bag of food? Also are there any methods to keep ants away from their food bag in the first place?
Throw it out.
I think the bigger problem is getting rid of the ants in your house, the ants in the cat's food are only a symptom of this root issue.
Ants are attracted to food smells, so try putting the (new!) food in an airtight container like a freezer-bag or a plastic container. That will also help the food to stay fresher.
Ants got into a fairly new $50 bag of prescription food, and I'm in no financial position at this time to throw it out. I immediately poured the food into a zip loc bag, which killed the ants (avalanche!). I was not about to pick out every ant carcass from 6-7 lbs. of food! Colander wouldn't work completely since the ants were sticking to the food and to every surface they touched, so I ended up pouring the food from one container to the next, with dead ants sticking to each container as the food was transferred to each one. Then I wiped the ants out of the containers and repeated the process until I felt the amount of ant remains was small enough. PS: I tried using compressed air, but it was about the same as the colander.
I don't use ant poison so there's no issue there, but that is a very important thing to consider if you find yourself in this position.