Mode-locked fiber laser technology to date has been limited to sub-3 μm wavelengths despite significant application-driven demand for compact picosecond and femtosecond pulse sources at longer wavelengths. Erbium-doped and holmium-doped fluoride fiber lasers incorporating a saturable absorber are emerging as promising pulse sources for 2.7-2.9 μm, yet it remains a major challenge to extend this coverage. Here, we propose a new approach using a dysprosium-doped fiber with frequency shifted feedback (FSF). Using a simple linear cavity with an acousto-optic tunable filter, we generate ∼33 ps pulses with up to 2.7 nJ energy and 330 nm tunability from 2.97 to 3.30 μm (∼3000-3400 cm-1) - the first mode-locked fiber laser to cover this spectral region and the most broadly tunable pulsed fiber laser to date. Numerical simulations show excellent agreement with experiments and also offer new insights into the underlying dynamics of FSF pulse generation. This highlights the remarkable potential of both dysprosium as a gain material and FSF for versatile pulse generation, opening new opportunities for mid-IR laser development and practical applications outside the laboratory.