Based on theoretical analysis and numerical simulation, the mechanism of self-pulsing operation of $2\text{-}\mu \mathrm{m}$ ${\mathrm{Tm}}^{3+}$ -doped fiber lasers is explored. A simplified rate-equation model is proposed to analyze stable operation of ${\mathrm{Tm}}^{3+}$ -doped fiber lasers. It is shown that the continuous-wave (CW) solution does not exist for certain pump intensities when excited-state absorption (ESA) is included. In numerical simulation, four energy-transfer processes are calculated to identify the origin of self-pulsing in ${\mathrm{Tm}}^{3+}$ -doped fiber lasers. The phonon-assisted ESA process ${}^{3}H_5\to {}^{3}H_4$ is identified as the key factor for self-pulsing in ${\mathrm{Tm}}^{3+}$ -doped fiber lasers, which confirms the absence of a CW solution in the theoretical analysis. The numerical simulation gives out a regular pulse train, whose characteristics are in excellent agreement with the experimental results. The impacts of ESA cross section and pump intensity on the self-pulsing characteristics are also investigated.