The victims were attacked FineFare Supermarket just after 9 a.m. Monday.
Two men in their 20s and a 17-year-old girl were rushed to Elmhurst Hospital.
None of their injuries were life-threatening.
The girl apparently was chased into the store by a man as part of the domestic dispute. The other two men were slashed while trying to help her.
At least two suspects were taken into custody and were being questioned.