With advancements in hardware and software, non-destructive radiometric analytical methods have become popular in a wide range of applications. A typical case is the study of the leaching process of metals from mineral ores and mine tailings. The objective of the current study was to develop a radiometric method based on neutron activation analysis (NAA), in particular, delayed gamma neutron activation analysis (DGNAA), to monitor the process of Mn and Zn leaching from Ti ore, Cu mine tailings, and Zn-Pb mine tailings. The DGNAA method was performed using a neutron source: a deuterium-tritium (D-T) neutron generator for Mn and a MARIA research nuclear reactor for Zn. Laboratory-scale Mn leaching from Ti ores, Cu tailings, and Zn-Pb tailings was investigated using delayed gamma-rays of ⁵⁶Mn (half-life of 2.6 h). The dissolution efficiencies of Mn were found to increase with interaction time and HCl concentration (1 to 5 M) and to vary with the leaching temperature (22.5 to 110 °C). Such results were found to agree with those obtained by total reflection X-ray fluorescence (TXRF) spectrometry for the same samples. ⁶⁵Zn (half-life of 244 days) was chosen to investigate real-time/online leaching of Zn in Ti ore, Cu tailings, and Zn-Pb tailings. During online monitoring, Zn recovery was also reported to increase with increased leaching time. After approximately 300 min of leaching, 80%, 79%, and 53% recovery of Zn in Zn-Pb tailings, Ti ore, and Cu tailings, respectively, were reported. Theoretically, developed mathematical prediction models for ⁶⁵Zn radiotracer analysis showed that the spherical diffusion model requires much less time to attain saturation compared to the linear diffusion model. The results of NAA for Zn were compared with those obtained by handheld X-ray fluorescence (handheld-XRF) and TXRF analysis. The analyzed samples encompassed leached Ti ore, Cu tailings, and Zn-Pb tailings which were subjected to different conditions of leaching time, temperature, and HCl concentrations. The XRF analysis confirmed that the leaching efficiencies of Zn rise with the increase in leaching time and HCl concentration and fluctuate with leaching temperature. The developed approach is important and can be applied in laboratories and industrial setups for online monitoring of the recovery of any element whose isotopes can be activated using neutrons. The efficiency of the metal-recovery process has a direct impact on the normal operation and economic advantages of hydrometallurgy.