B737 Undifferentiated or Other Model
Flight Crew Air Transport Pilot (ATP)
Flight Crew Type 1140
Communication Breakdown
ATC Issue All Types; Conflict Ground Conflict; Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Other / Unknown; Ground Incursion Runway
Air Traffic Control Provided Assistance; Air Traffic Control Separated Traffic; Flight Crew Requested ATC Assistance / Clarification
Airport; Weather
After touchdown during rollout; heavy rain was encountered. ATC gave us clearance to exit the runway at a specified taxiway; I could not discern which taxiway was the correct taxiway; or even exactly where the taxiways were. I had my windshield wipers on high/fast. While slowing and identified where I was supposed to exit; ATC cleared a flight for takeoff. We had not even started our exit off the runway; nor did I know where exactly I was exiting. After the takeoff clearance issued; I tried to alert ATC we were on the runway; [departing aircraft] was simultaneously reading back their clearance. After [departing aircraft] read back their takeoff clearance; I told them to 'cancel their takeoff clearance; [we are] is still on the runway'. ATC; then asked [departing aircraft] to taxi down the runway and make the first available exit.
B737 Captain reported that after landing; they were still taxiing on the runway when another aircraft was given clearance for takeoff.