A 976-nm pulse-type switchable mode-locked fiber laser is experimentally demonstrated, for the first time to our knowledge, with a single mode fiber-graded index multimode fiber-single mode fiber (SMF-GIMF-SMF) structure-based saturable absorber (SA). The GIMF is bent into a given state to strengthen its effect on establishing mode-locking. By adjusting the intra-cavity polarization controller, the switching between dissipative solitons (DSs) and noise-like pulses (NLPs) can be achieved. Meanwhile, we also realize a second harmonic mode-locking (HML) in the same laser cavity. The laser provides a solution to realize 976 nm mode-locking operation with a simple and low-cost configuration and can serve as a potential tool for various applications.