We demonstrated an all-fiber multiwavelength mode-locking thulium-doped fiber laser employing a cascaded single-mode step-index multimode-graded-index multimode single-mode-fiber (SMF-SIMF-GIMF-SMF) saturable absorber (SA). Based on the linear and nonlinear multimode interference effect of the proposed device, this structure can act both as a filter and as a SA. A stable triwavelength (1857/1897/1934 nm) mode-locking operation with the adjacent wavelength interval of approximately 40 nm was obtained. The triwavelength mode locking can also be quickly switched either pair-by-pair or one-by-one by adjusting the polarization controller properly. Our results indicate that the SMF-SIMF-GIMF-SMF structure provides a simpler and more compact solution for switchable multiwavelength mode locking in fiber lasers.