We have developed a stable, high-power, single-frequency optically pumped external-cavity semiconductor laser system and generate up to $125\mathrm{mW}$ of power at $253.7\mathrm{nm}$ using successive frequency doubling stages. We demonstrate precision scanning and control of the laser frequency in the UV to be used for cooling and trapping of mercury atoms. With active frequency stabilization, a linewidth of $<60\mathrm{kHz}$ is measured in the IR. Doppler-free spectroscopy and stabilization to the $6^1{S}_0–6^3{P}_1$ mercury transition at $253.7\mathrm{nm}$ is demonstrated. To our knowledge, this is the first demonstration of Doppler-free spectroscopy in the deep UV based on a frequency-quadrupled, high-power ( $>1\mathrm{W}$ ) optically pumped semiconductor laser system. The results demonstrate the utility of these devices for precision spectroscopy at deep-UV wavelengths.