We propose a single-wavelength-tunable and dual-wavelength-switchable Tm-doped fiber soliton laser with single-walled carbon nanotubes. The laser can deliver single-wavelength mode-locked pulse tunable from 1892 nm to 1924 nm. Dual-wavelength mode-locking operation can also be achieved by increasing pump power and rotating the polarization controller (PC), meanwhile the wavelength can be switched between 1883/1894 nm and 1905/1910 nm. Both the tunable and switchable operations are realized with great ease by solely adjusting the parameters of PC. The proposed Tm-doped fiber laser can operate in two mode-locking states, which is helpful for further understanding of the mode-locking mechanism and useful for practical applications.