We report on a systematic analysis of the spin and superorbital modulations of the high-mass X-ray binary 4U 0114+650, which consists of the slowest spinning neutron star known. Utilizing dynamic power spectra, we found that the spin period varied dramatically during the RXTE ASM and Swift BAT observations. This variation consists of a long-term spin-up trend, and two ~1,000 day and one ~600 day random walk epochs previously, MJD 51,000, ~MJD 51,400-52,000, and ~MJD 55,100-56,100. We further found that the events appear together with depressions of superorbital modulation amplitude. This provides evidence of the existence of an accretion disk, although the physical mechanism of superorbital modulation remains unclear. Furthermore, the decrease of the superorbital modulation amplitude may be associated with the decrease of mass accretion rate from the disk, and may distribute the accretion torque of the neutron star randomly in time.