Are you sure it's a cutworm, because I am very fond of blaming everything wrong with a dahlia on slugs and this is no exception!
Not sure what kind of cutworms you have in your location, but this dealy below would be awfully tedious on 40 plants. And even worse in my phlox which they invade every year about now...

Here is a link that might be useful: cutworm device

I am raising dahlia plants in raised beds and they were doing so well. Now that they are getting buds they look like they are rotting at the surface. If I touch the plants they fall over. I did not stake the plants in the spring, which I should have, but this seems like either bugs or they are to wet. We have been getting lots of rain but the beds drain very well. I have about 25 plants and I am just sick about it. I have been staking the plants being very carful not to spear a tuber. Help!!!