A method of releasing a safety joint in a subterranean well can include disconnecting a tubular string at the safety joint without rotation of the tubular string. A safety joint for use in a subterranean well can include sections which are separated from each other in response to a predetermined number of relative longitudinal and non-rotational displacements between the safety joint sections. Another method of releasing a safety joint in a subterranean well can include fully actuating a jar multiple times, the jar being interconnected in a same tubular string with the safety joint, and then disconnecting the tubular string at the safety joint in response to non-rotational displacement of the tubular string.