Answer: I would not recommend cutting them down. Ants do not hurt flowers and are not usually harmful in the garden. But, the ants might be attracted to the flowers if there is a large population of aphids on the flowers.
Aphids are soft bodied insects that cluster on the tender growing tips of the plants. If you see aphids, they can be knocked down with a spray of water from the garden hose, or you could spray them with insecticidal soap, or you could wait for ladybugs to appear and control the aphids naturally.
If the ants are coming into your house from the garden, then you might find the control information at the following web page helpful.
You could also consult with your local Cornell cooperative extension if you are still concerned about the ants. I hope this helps.
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