SF50 pilot reported failing to remove the AOA cover prior to flight. After takeoff; the pilot heard a noise that did not dissipate upon raising the landing gear and decided to perform an air turnback. Due to having no airspeed indication the pilot had difficulty in controlling the aircraft; which led to a runway excursion.

Narrative

Departed ZZZ around XA:50 for an IFR flight to ZZZ1. Conditions were VMC. Received a report while taxiing from Ground Controller that there was some possible FOD" reported on the runway. I acknowledged that information and continued to taxi. We were cleared for takeoff and began to hear a noise that sounded like gravel hitting the gear. After takeoff I raised the landing gear and the noise did not stop. I was cleared to communicate with ZZZ Departure but I told Tower that I was going to head back in to determine the source of the noise.As I turned to make a left downwind; the stall warning sounded and stick shaker activated. I used the AP (Autopilot) disconnect button to regain control of the plane and headed back to Runway XX. I made a short base turn as it was difficult to control the plane and had no indication of speed as it was reading 200+ kt. I turned to short final and landed heavy and fast. The plane bounced a couple of times and then skidded off the runway. No damage to the airport. Once I landed I realized that I had failed to remove the AOA cover which is what caused the stall readings. The plane has been recovered and stored in a hangar on-site."