Gardeners loathe these critters. We haven't had too much trouble with them in our food crops (knock on wood), but last summer they all but thwarted our efforts to make a sunflower house. They'd eat through every new sprout we planted, over and over.
There are several ideas out there for helping control cutworms. Here's a simple one. Make a collar out of a cup by cutting out the bottom, and put it over your baby plant. Or use a toilet paper tube (we all have plenty of those, right?). Plastic containers are good, too, but they will be harder to cut away when your plant outgrows its collar. Check out all these ideas for making cutworm collars, and choose one or two. Protect those babies you worked so hard to get ready to plant in the garden!