We report a widely tunable pulsed dysprosium (Dy) -doped fluoride fiber laser within a 545 nm continuous wavelength range around 3 μm, where a home-made random Raman fiber laser (RRFL) at 1.690 μm acts as the pump, and a commercial InAs saturable absorber (SA) is adopted as the Q-switcher. The designed RRFL, excited by a 1.055 μm ytterbium-doped fiber oscillator, can provide the 8 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> order Stokes emission at 1.690 μm with a high spectral purity of 98.6% and a maximum output power of 14.4 W. Feeding it to a Dy cavity involving an InAs SA and a ruled diffraction grating in a Littrow configuration, stable Q-switching can be initiated and tuned within the continuous/total range of 2.775∼3.320 μm (545 nm)/2.765∼3.338 μm (573 nm), an extension of 50% over the prior 370 nm record [Opt. Lett., vol. 44, no. 9, pp. 2322-2325, 2019], representing the widest level to date from a pulsed rare-earth-doped laser at any wavelengths, to the best of our knowledge. When the wavelength is tuned to 2.992 μm, a maximum average power of 106 mW with 460 ns pulse width, 125 kHz repetition rate, and 0.85 μJ pulse energy is achieved. This work marks the first pulsed Dy-doped fluoride fiber laser pumped at ∼1.7 μm while exhibiting the utility of InAs in pulse generation at the wavelengths of 3∼3.4 μm for the first time, to the best of our knowledge. The demonstration highlights the great potential of ∼1.7 μm pumped Dy-doped fluoride fiber laser as a platform for developing widely tunable pulsed sources in the 3 μm region of the mid-infrared.