We investigate the quantum speed limit time for neutral $K$ and $B$ mesons, both single as well as correlated, within the framework of open quantum systems. The role of coherence-mixing on quantum speed limit is studied. The impact of decoherence and CP violation on quantum speed limit time is also investigated. Quantum speed limit time increases with the evolution time for the single mesons. Correlated mesons are seen to be evolved faster, suggesting that quantum correlations can speed up the evolution.