The radio-emitting neutron star population encompasses objects with spin periods ranging from milliseconds to tens of seconds. As they age and spin more slowly, their radio emission is expected to cease. We present the discovery of an ultra-long-period radio-emitting neutron star, PSR J0901-4046, with spin properties distinct from the known spin- and magnetic-decay-powered neutron stars. With a spin period of 75.88 s, a characteristic age of 5.3 Myr and a narrow pulse duty cycle, it is uncertain how its radio emission is generated and challenges our current understanding of how these systems evolve. The radio emission has unique spectro-temporal properties, such as quasi-periodicity and partial nulling, that provide important clues to the emission mechanism. Detecting similar sources is observationally challenging, which implies a larger undetected population. Our discovery establishes the existence of ultra-long-period neutron stars, suggesting a possible connection to the evolution of highly magnetized neutron stars, ultra-long-period magnetars and fast radio bursts.