Superconducting (SC) state has spin and orbital degrees of freedom, and spin-triplet superconductivity shows multiple SC phases because of the presence of these degrees of freedom. However, the observation of spin-direction rotation occurring inside the SC state (SC spin rotation) has hardly been reported. Uranium ditelluride, a recently found topological superconductor, exhibits various SC phases under pressure: SC state at ambient pressure (SC1), high-temperature SC state above 0.5 gigapascal (SC2), and low-temperature SC state above 0.5 gigapascal (SC3). We performed nuclear magnetic resonance (NMR) and ac susceptibility measurements on a single-crystal uranium ditelluride. The b axis spin susceptibility remains unchanged in SC2, unlike in SC1, and decreases below the SC2-SC3 transition with spin modulation. These unique properties in SC3 arise from the coexistence of two SC order parameters. Our NMR results confirm spin-triplet superconductivity with SC spin parallel to b axis in SC2 and unveil the remaining of spin degrees of freedom in SC uranium ditelluride.