We demonstrate, for the first time, use of a stretched single mode-graded-index multimode-single mode fiber (SMF-GIMF-SMF) structure as a saturable absorber (SA) for a passively mode-locked Tm fiber laser. Such an all-fiber SA was based on the nonlinear multimode interference (NL-MMI). Stable fundamentally mode-locking operation was obtained at a pump threshold of 100mW. The output soliton pulses had a center wavelength, spectral width, pulse duration, and repetition rate of 1931 nm, 3.77 nm, 1.2ps, and 19.94 MHz, respectively. Furthermore, the SMF-GIMF-SMF structure can also be used as a filter to tune the laser. Continuously tunable mode-locking was experimentally demonstrated only by varying the stretched length of GIMF. Our results indicate that the stretched SMF-GIMF-SMF structure could serve as a SA together with a bandpass filter, which makes it advantageous for wavelength-tunable mode locking lasers.