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Twisted van der Waals homo- and hetero-structures have aroused great attentions due to their unique physical properties, providing a new platform to explore the novel two-dimensional (2D) condensed matter physics. The robust dependence of phonon vibrations and electronic band structures on the twist angle has been intensively observed in transition metal dichalcogenide (TMD) homo-structures. However, the effects of twist angle on the lattice vibrational properties in the TMD heterostructures have not caused enough attention. Here, we report the distinct evolutions of Raman scattering and the underlying interlayer interactions in the twisted WS2/MoS2 heterostructures. The shifts and linewidths of E2g(Γ) and A1g(Γ) phonon modes are found to be twist angle dependent. In particular, analogous to that of the twisted TMD homostructures, the frequency separations between E2g(Γ) and A1g(Γ) modes of MoS2 and WS2 in the twisted heterostructures varying with twist angle correlate with the interlayer mechanical coupling, essentially originating from the spacing-related repulsion between sulfur atoms. Moreover, the opposite shift behaviors and broadening of A1g(Γ) modes caused by charge transfer are also observed in the twisted heterostructures. The calculated interlayer distances and band alignment of twisted WS2/MoS2 through density functional theory further evidence our interpretations on the roles of the interlayer mechanical coupling and charge transfer in variations of Raman features. Such understanding and controlling of interlayer interaction through the stacking orientation are significant for future optoelectronic device design based on the newly emerged 2D heterostructures.