I'd say slugs/snails or cutworms.

...or Black Vine Weevils...at the edges.

Thank you so much!..I went out and bought a pkg of "Ortho Bug-Geta"..is suppose to kill slugs and snails...Hope it works!..Thank you again!

Another vote for cutworms here, so I would suggest an insecticide. The gray or brown worms live in the soil by day and feed by night. A liquid is best since it will get into the soil where they are hiding, or go out at night and you might catch them in the act.

Sevin dust sprinkled under the clump will also eliminate them.

Yup!! it's cutworms.. I just dug a little aroung the plant and found them......Thank you so much for everyone's help..