Air carrier First Officer reported a moderate/severe turbulence encounter on climb. Crew diverted and aircraft was taken out of service.

Narrative

We were operating Flight ABCD ZZZ-ZZZZ; during taxi out departing aircraft were reporting wind shear on departure but the Tower was not reporting any wind shear on departure but was reporting +/- 15th on final for XXL. Captain was PF; he asked me run wind shear numbers for takeoff for Runway XXR; we briefed the RTO (Rejected Takeoff) again and wind shear. Takeoff roll and liftoff were normal. Once airborne we were on the ZZZZZ X departure which has a 210kt restriction on the first fix. At thrust reduction altitude we retracted flaps from 2 to 1 but Captain held TOGA power for a little longer due to +/- 20kt airspeed fluctuations. After reducing to CLB thrust we hit what we believe to be severe turbulence; Captain called for flaps 0 due to rapidly increasing airspeed; this was followed by our Flight Directors to kick off at the same time we got a momentary flap over speed alarm all while Captain fighting to maintain control as the aircraft was trying to roll rapidly. During this time the engines had rolled back to flight idle; regardless of the thrust levers being in the CL detent. Captain increased to FLX/MCT (Maximum Continuous Thrust) with zero change to engine thrust; he then elected to go back to TOGA power at which time the engines responded with full power as the airplane was approaching Vls. We had deviated slightly off of the SID track and I called Departure to let them know about the turbulence we had encountered. We ended up accelerating to approximately 320 at around 3000' because we wanted to get our airspeed back and were concerned what would happen once we reduced the levers to CL again. I told ATC what was happening and they gave us a vector and altitude to fly; no emergency was declared. After reaching smooth air at around 4500' we ran after takeoff checklist and proceeded on route. The rest of the departure and flight was normal. Once we reached cruise Captain contacted Dispatch and Maintenance to inform them of what happened with the turbulence and engine roll back. After taking a break around the 2 hour mark; we coordinated with the rest of the crew on their thoughts of how extreme the turbulence was using our charts in the FOM. Once we determined it was moderate; borderline severe; Captain called Dispatch and we were told to divert to ZZZ1 so the plane could be taken out of service. The arrival and landing were normal. We were met by Maintenance at the gate so they could get the information straight from us; Captain filled out the logbook and we collected our things to leave the airplane. We were then placed on the continuing flight as DH to resume our pairing; half way to ZZZZ we received notice we would be DH back to ZZZ1 the following morning and removed from our pairing.