Question
Some critter is cutting my impatiens at the base of the stem. Each day I find that more stems have been cut. The plants are healthy and in full bloom. It looks similar to a forest being cleared.

Answer
My guess is "CUTWORMS".
Options for controlling cutworms:
Place cornmeal or bran meal around the plants and leading away from the plants. the cutworms will eat the meal which will then absorb moisture, swell, and kill them.
You can hand pick them at night, if you are not too squeamish about touching them. Look around the base of the plant and just below the soil surface. They are a plump, soft bodied, dull grayish or brownish caterpillar that is 1 to 2 inches long.  You usually find them in a curled position.
Creating barriers to keep them away from the plants will also help.
Diatomaceous earth, milk carton collars, paper collars, wood ashes, and any other thing you can put around to stop them from reaching the plants. They can't eat them if they can't get to them.
These larvae are from moths that produce several times a year. The worst time is in the spring. They are less apparent as the season progresses.

One other possibility is rabbits. The cut will be angled, and the damage more severe.