We report the first demonstration of a microresonator-based tunable mode-locked frequency comb source. We achieve a mode-hop-free tuning range of 16 GHz by simultaneously tuning both the pump laser and the cavity resonance while keeping the system in a multi-soliton mode-locked state. The optical spectrum spans 2520-4125 cm-1 (2.425-3.970 μm) pumping at 3508 cm-1 (2.850 μm) in a silicon microresonator with a comb line spacing of 4.23 cm-1 (127 GHz). Our scanning technique can be used to increase the effective resolution of the microresonator-based comb spectroscopy. As a proof-of-principle demonstration, we record the absorption spectrum of the rovibrational transitions of the υ3 and υ2+(υ4+υ5)+0 bands of acetylene. We measure absorption features as narrow as 0.21 cm-1 (6.4 GHz) full width at half-maximum at a frequency sampling step of 80 MHz.