Air carrier Captain reported severe turbulence during cruise flight when deviating around thunderstorms; resulting in an altitude and heading deviation. The flight returned to the clearance and no injuries were reported.

Narrative

On Day 0 around XA:43 Aircraft X encountered severe turbulence flying from EYW - ZZZ. We were originally filed for FL350 but once airborne we were informed that our new final altitude would be FL330. On the climb out and during cruise my First Officer (FO) and I were requesting headings to avoid cumulus buildups along our route of flight. The fasten belt sign was on and our flight attendants were seated. Once we were clear of the buildups we were direct DUCEN intersection and our flight attendants began their cabin service with the carts out. Shortly after that point we transitioned from VMC to IMC. My FO and I both had our radars on throughout the flight and at that point; both were set to 100 nm rings. We both didn't see anything on our radars and the ride was smooth. Shortly after; I sized down to the 50nm ring and saw a tiny yellow radar spot just in front of our aircraft. Once I took note of it; I mentioned it to my FO and then sized down to 12.5nm rings. At 12.5 nm I was able to see half of a radar sweep and then at 5nm I saw a full sweep. There was a small cell that was outlined in yellow and in the middle was all red. By the time we requested a right deviation the aircraft started shaking violently. The Autopilot disengaged and I disconnected the auto throttles. I took command of the aircraft and fought to keep us stable. I then began a right turn to escape the turbulence. Our airspeed was at Mach .74 and our airspeed was fluctuating rapidly. Once we escaped the turbulence I noted a loss of 500'. We reported our severe turbulence to ATC and checked on the cabin. Our flight attendants and passengers were ok and no injuries were reported. There weren't any EICAS messages either. The Autopilot and auto throttles were able to reengage.The turbulence was encountered east of MATLK intersection and lasted for approximately 30 seconds. Airspeed increased but we did not overspeed.