Contemporary attempts to explain the existence of ultra-high energy cosmic rays using plasma-based wakefield acceleration deliberately avoid non-Standard Model particle physics. However, such proposals exploit some of the most extreme environments in the Universe and it is conceivable that hypothetical particles outside the Standard Model have significant implications for the effectiveness of the acceleration process. Axions solve the strong CP problem and provide one of the most important candidates for Cold Dark Matter, and their potential significance in the present context should not be overlooked. Our analysis of the field equations describing a plasma augmented with axions uncovers a dramatic axion-induced suppression of the energy gained by a test particle in the wakefield driven by a particle bunch, or an intense pulse of electromagnetic radiation, propagating at ultra-relativistic speeds within the strongest magnetic fields in the Universe.