Sergeant Matthew Oehler, public information officer for South Salt Lake Police, said they were called to the 7-11 located at 2102 South State Street just before midnight.
When officers arrived they found three individuals had been stabbed, two males and one female.
All three were taken to area hospitals, one in critical condition and two in stable.
The investigation is still active and police believe the crime happened at one of the nearby homes. No arrests have been made. Anyone with information is asked to call South Salt Lake Police at 801-840-4000.