When facing certain problems in science, engineering or technology, it is not enough to find a solution, but it is essential to seek and find the best possible solution through optimization. In many cases the exact optimization procedures are not applicable due to the great computational complexity of the problems. As an alternative to exact optimization, there are approximate optimization algorithms, whose purpose is to reduce computational complexity by pruning some areas of the problem search space. To achieve this, researchers have been inspired by nature, because animals and plants tend to optimize many of their life processes. The purpose of this research is to design a novel bioinspired algorithm for numeric optimization: the Mexican Axolotl Optimization algorithm. The effectiveness of our proposal was compared against nine optimization algorithms (artificial bee colony, cuckoo search, dragonfly algorithm, differential evolution, firefly algorithm, fitness dependent optimizer, whale optimization algorithm, monarch butterfly optimization, and slime mould algorithm) when applied over four sets of benchmark functions (unimodal, multimodal, composite and competition functions). The statistical analysis shows the ability of Mexican Axolotl Optimization algorithm of obtained very good optimization results in all experiments, except for composite functions, where the Mexican Axolotl Optimization algorithm exhibits an average performance.