In classical general relativity there is black hole area theorem due to Hawking, which states that given reasonable conditions on matter sources (specifically, the null energy condition), the area of event horizon is non-decreasing with time. So, assuming that those conditions hold, we cannot destroy a black hole, but we can e.g. merge it with another black hole, so that instead of two we would only have one larger black hole.
Quantum fields often do violate the null energy condition and so black hole evaporation through Hawking radiation does not contradict this theorem, however for stellar mass black holes the timescales for such evaporation exceed the current age of the Universe by many orders of magnitude.
If such evaporation seems too slow, then it is possible to greatly increase the rate of black hole's mass loss from Hawking radiation. This could be achieved by constructing around the black hole a system that facilitates efficient removal (and subsequent dissipation) of radiative thermal energy from the near horizon region.
The basic principle is well known in thermal engineering: if the heat dissipation is too slow, put in a heat sink or a heat exchanger, but of course there are some subtleties.
Very close to black hole event horizon Hawking radiation has an almost perfect black body spectrum. However by the time this radiation reaches outside observers its spectrum is modified. This is because the gravitational field of a black hole serves as a barrier to radiation propagating from the black hole horizon: it partially transmits radiation and partially reflects it back onto horizon. Moreover, there are near horizon modes of radiation that do not reach the outer region at all. An optical analogue would be the total internal reflection phenomenon, with photon sphere serving as a (smeared) interface between optically dense near horizon (effective) medium and the almost vacuum outer region.
Using the pair creation metaphor, we can say that some of photons that are created at the horizon never escape and are subsequently reabsorbed by the black hole. But what if we can capture those photons before they are reabsorbed and remove their energy by other means, such as through thermal conduction by material of a “heat sink” around the black hole or via some active heat exchange system? Then it would be possible to increase the “thermal output” of the black hole, and the closer to black hole horizon we can capture those photons, the greater the increase would be. Of course, constructing material structure very close to black hole horizon is no small engineering challenge, and in fact there could be some fundamental limitations on how close to the horizon this structure could be, how efficiently it could absorb Hawking radiation quanta and how efficient is the energy transfer within this structure. Overall the black hole mass loss could be greatly increased relative to “unoptimized” Hawking radiation, but those “fundamental limitations” would not allow us to reduce the black hole lifetime arbitrarily.
References
The process of “mining energy from black hole” has been suggested by Unruh & Wald in [$1$]. In [$2$] there is a pop-sci account and a discussion of limitations. Recent paper [$3$] provides an estimate of black hole mass loss increase of $\approx 2 \cdot 10^2$ achieved
by a perfectly absorbing screen placed at $\delta r = 10^{-4} r_s$ away from the black hole.
Unruh, W. G., & Wald, R. M. (1983). How to mine energy from a black hole. General Relativity and Gravitation, 15(3), 195-199, doi:10.1007/BF00759206.
Brown, A. (2015). Can We Mine a Black Hole? Scientific American, 312(2), 44-49, free PDF.
Saraswat, K., & Afshordi, N. (2021). Extracting Hawking radiation near the horizon of AdS black holes. Journal of High Energy Physics, 2021(2), 1-47, doi:10.1007/JHEP02(2021)077, arXiv:2003.12676.
