OK sorry, I didn't quite have the picture. Yes it sounds like something is eating your plants. I still don't think the ants are likely the original cause. Cutworms can cause damage to the stems just below ground like that. If it is that, you can dig around the base of the plant in the daytime and usually find the worm in the soil near the plant. If you scroll down, this has pictures of what they look like:
They feed at night, so you could also go out at night with a flashlight and look for them.
If you have cutworms, if you plant your plants with a stiff paper or tin foil collar around them, but not touching or put a couple toothpicks in the ground next to them, it stops the cutworms from getting to your plants.