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We study the spatial rock-paper-scissors game with adaptive mutation which may describe imitation behaviors of two competing species. We introduce an adaptive mutation where one of the species may tend to mutate the other by implementing a fundamental mutation mechanism with respect to local fitness of two competing species by comparing payoffs of its origin with the updated one when it mutates to the other. By means of Monte Carlo simulations, we show that species coexistence can be promoted by the intensification of adaptive mutation at certain high mobility regimes which lead the extinction traditionally, even if extremely high mobility results in the extinction as well. In addition, by measuring the extinction probability for extensive scales of spatial domains, we also found that the critical mobility to lead extinction is shifted according to the rate of adaptive mutation. Ultimately, our findings may indicate that adaptive mutation can be a significant role to maintain coexistence for moderately strong individuals' mobilities. [ABSTRACT FROM AUTHOR]