We report the hydrostatic pressure induced two topological phase transitions in strong spin-orbit coupled material $\mathrm{TlBi}{\mathrm{S}}_{2}$ at room temperature. Frequencies of the ${\mathrm{A}}_{1\mathrm{g}}$ and ${\mathrm{E}}_{\mathrm{g}}$ phonons are observed to increase monotonically up to $\ensuremath{\sim}4.0\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$, but with a clear slope change in ${\mathrm{A}}_{1\mathrm{g}}$ mode at $\ensuremath{\sim}1.8\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. Interestingly, there are two clear anomalies noticed in phonon linewidths of ${\mathrm{E}}_{\mathrm{g}}$ mode at pressures $\ensuremath{\sim}0.5$ and $\ensuremath{\sim}1.8\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. Such anomalies are evidence of isostructural electronic transitions associated with unusual electron-phonon coupling. The high-pressure synchrotron powder diffraction and Raman show a first-order phase transition above 4 GPa. First-principles density functional theory-based calculations of electronic band structure, topological invariant ${\mathbb{Z}}_{2}$ and mirror Chern number ${n}_{M}$ reveal that the phonon anomalies at $\ensuremath{\sim}0.5$ and $\ensuremath{\sim}1.8\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ are linked to the band inversions at $\mathrm{\ensuremath{\Gamma}}$ and $F$ points of the Brillouin zone respectively. The first band inversion at $\mathrm{\ensuremath{\Gamma}}$ point at $\ensuremath{\sim}0.5$ GPa changes the ${\mathbb{Z}}_{2}$ from 0 to 1 leading to the transition of $\mathrm{TlBi}{\mathrm{S}}_{2}$ system into a topological insulator. The second band inversion at $F$ point at $\ensuremath{\sim}1.8\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ results in ${n}_{M}=2$, revealing a transition to a topological crystalline insulating state. Therefore the applied pressure systematically tunes the electronic states of $\mathrm{TlBi}{\mathrm{S}}_{2}$ from a normal semiconductor to a topological insulator and finally into a topological crystalline insulator at two distinct pressures of $\ensuremath{\sim}0.5$ and $\ensuremath{\sim}1.8\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ respectively, before undergoing a structural phase transition at $\ensuremath{\sim}4\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$.