Diversity has been widely studied in software testing as a guidance towards effective sampling of test inputs in the vast space of possible program behaviors. However, diversity has received relatively little attention in mutation testing. The traditional mutation adequacy criterion is a one-dimensional measure of the total number of killed mutants. We propose a novel, diversity-aware mutation adequacy criterion called distinguishing mutation adequacy criterion, which is fully satisfied when each of the considered mutants can be identified by the set of tests that kill it, thereby encouraging inclusion of more diverse range of tests. This paper presents the formal definition of the distinguishing mutation adequacy and its score. Subsequently, an empirical study investigates the relationship among distinguishing mutation score, fault detection capability, and test suite size. The results show that the distinguishing mutation adequacy criterion detects 1.33 times more unseen faults than the traditional mutation adequacy criterion, at the cost of a 1.56 times increase in test suite size, for adequate test suites that fully satisfies the criteria. The results show a better picture for inadequate test suites; on average, 8.63 times more unseen faults are detected at the cost of a 3.14 times increase in test suite size.