We have implemented wavelength-tunable and dual-wavelength in an ytterbium-doped passively mode-locked fiber laser using a single mode-graded index multimode-single mode fiber (SMF-GIMF-SMF) device as the saturable absorber (SA) without additional components. Such an all-fiber SA device exhibits fantastic properties with a large modulation depth of 22.9%, a small saturation fluence of 8.3 μJ/cm2, and the transmission curve with a capacity of gain-flattening, which are suitable for the tunable mode-locking generation. Benefiting from the intracavity birefringence-induced filtering effect of the laser cavity, tuning and dual-wavelength operations are obtained. For the tuning operation, the central wavelength of the dissipative solitons (DSs) can be tuned from 1028.5 to 1074.4 nm, with the pulse duration of tens of picoseconds. For the dual-wavelength mode-locking operation, the central wavelengths of dual-wavelength can be switched from 1032.3/1054.1 nm to 1049.3/1072.6 nm. Our results indicate that the SMF-GIMF-SMF device provides a novel platform for wavelength-tunable and dual-wavelength mode-locking in Yb-doped fiber lasers.