A method of freeing a pipe stuck in a subterranean well can include determining a location of a portion of the pipe stuck in the well, and penetrating and/or heating a sidewall of the pipe portion with a beam of light. A system for freeing a pipe stuck in a subterranean well can include a tool deployed into a portion of the pipe stuck in the well by a differential pressure from a wellbore to a formation penetrated by the wellbore. A beam of light emitted from the tool penetrates the pipe portion. Another method of freeing a pipe stuck in a subterranean well can include determining a location of a portion of the pipe which is biased against a wall of a wellbore by differential pressure, and directing a beam of light to the pipe portion.