During the service, the turbine blades of aero-engines are subjected to a complex and ever-changing combination of temperature and stress, resulting in severe cyclic temperature/strain damages and thermal-mechanical fatigue (TMF) failures of the alloy. In this work, in-phase (IP) TMF tests under 600-1000^oC were conducted on a newly developed fourth-generation single-crystal superalloy. The alloy's fracture characteristics and comprehensive damage mechanisms were examined via SEM, EBSD, and TEM. The results showed that when the strain range increased, the fatigue life of the experimental alloy noticeably decreased, and the hysteresis loop clearly opened. Stress response behaviors shifted from cyclic softening at high temperatures and cyclic hardening at low temperatures into a dominant characteristic of cyclic stabilizing. The fracture surfaces of alloys displayed ductile features after fatigue fracture under various circumstances, and the area fraction of dimples reduced with increasing strain amplitude. When the strain amplitude was low, the alloy was mainly subjected to oxidation damage, accompanied with a certain degree of creep damage. In contrast, the dominant deformation mechanism of the alloy was dislocation slipping in γ matrix and Orowan by-passing through γ' particles. As the strain amplitude increased to higher levels, the alloy was subjected to severe plastic deformation damage, while the degree of oxidation damage had been alleviated. Under this condition, the interfacial dislocations could shear into the γ' phase with the generated stacking fault or anti-phase boundary. Notably, no recrystallization grains or deformation twins were formed in the DD91 alloy during the IP-TMF experiments at different mechanical strain amplitudes.