Here we developed a novel wavelength-switchable visible continuous-wave (CW) Pr³⁺:YLF laser around 670 nm. In single-wavelength laser operations, the maximum output powers of 2.60 W, 1.26 W, and 0.21 W, the maximum slope efficiencies of 34.7%, 27.3%, and 12.3% were achieved with good beam qualities (M² < 1.6) at 670.4 nm, 674.2 nm, and 678.9 nm, respectively. Record-high output power (2.6 W) and record-high slope efficiency (34.7%) were achieved for the Pr ³⁺:YLF laser operation at 670.4 nm. This is also the first demonstration of longer-wavelength peaks beyond 670 nm in the ³P₁→³F₃ transition of Pr³⁺:YLF. In multi-wavelength laser operations, the dual-wavelength lasings, including 670.1/674.8 nm, 670.1/679.1 nm, and 675.0/679.4 nm, were obtained by fine adjustment of one/two etalons within the cavity. Furthermore, the triple-wavelength lasings, e.g. 672.2/674.2/678.6 nm and 670.4/674.8/679.4 nm, were successfully demonstrated. Moreover, both the first-order vortex lasers (LG₀⁺¹ and LG₀^-1 modes) at 670.4 nm were obtained by off-axis pumping.