At 02.10 hours on 11 June 1942, U-504 fired a spread of four G7a torpedoes at the unescorted Crijnssen (Master Willem van der Giessen) from a distance of 2200 meters and hit her with two of them under the bridge and further aft about 85 miles southwest of Grand Cayman Island. About 15 minutes before the attack, the ship had received a warning about a U-boat in the area and her master tried to evade the danger by heading west and zigzagging at full speed immediately, but the U-boat was already chasing her and Poske had to act quickly by turning U-504 around to fire all bow torpedo tubes at the fast vessel from a rather great distance when the Germans discovered that both stern torpedo tubes were out of order just moments before being in a favorable position to fire them. It took some time to stop the ship after the hits because the men on watch below had to evacuate the engine room when it was flooded and the engines ran until the chief and third engineer managed to close the main steam valves to the boilers. While the ship began to settle slowly by the bow, the crew, passengers and gunners abandoned ship in the three lifeboats on the port side (#4, #5 and #6), a gig and boat #1 which was the only one remaining on the starboard side because the explosions had completely destroyed boat #2 and damaged the davits of boat #3. The radio operators were unable to send distress signals because both aerials came down and the emergency wireless set had been in the destroyed lifeboat. Only the master, the second officer and two stewards remained behind to carry out a search for missing crew members and then left on a raft. In the meantime, the U-boat fired a coup de grâce from one of the repaired stern torpedo tubes but missed at 02.22 hours. Poske observed that there were still people aboard, surfaced one hour after the initial attack and at 03.31 hours fired a second coup de grâce from a reloaded bow torpedo tube which hit the Crijnssen on the port side just aft of the bridge and caused the ship to sink within seven minutes after capsizing to port. One crew member was lost.

The ship was repatriating twelve survivors from the Sylvan Arrow, which had been sunk by U-155 (Piening) on 20 May 1942, ten survivors from the Lise, which had been sunk by U-69 on 12 May 1942 and one survivor from the American steam tanker T.C. McCobb, which had been sunk by the Italian submarine Pietro Calvi (Olivieri) on 31 March 1942. The lifeboats lost contact to each other the following night, but the third officer in charge of boat #6 with an auxiliary engine tried to locate the others at daylight. The survivors in his boat, boat #4 and the gig were picked up the same day by the Lebore which was herself sunk by U-172 (Emmermann) three days later, but all shipwrecked from Crijnssen survived the second sinking. The master and three crew members were rescued from their raft by J.A. Mowinckel in 18°29N/85°54W in the evening of 11 June and were landed at Aruba on 16 June. The boat #1 in charge of the chief engineer with nine occupants made landfall at Punta Herrero Lighthouse on Espirito Santo Bay after several days, from where they were taken to Cozumal and then by plane to Mérida, arriving on 24 June. The 31 survivors in boat #5 also reached the Yucatan coast and were first taken to Xcalak by the Mexican sailing vessel Quintana Roo and then to Mérida, arriving on 26 June. All survivors in Mexico were later flown from Chetumal to Brownsville, Texas.