Deep neural network (DNN) mutation analysis is a promising approach to evaluating test set adequacy. Due to the large number of generated mutants that must be tested on large datasets, mutation analysis is costly. In this paper, we present a technique, named DM#, for accelerating DNN mutation testing using Fourier analysis. The key insight is that DNN outputs are real-valued functions suitable for Fourier analysis that can be leveraged to quantify mutant behavior using only a few data points. DM# uses the quantified mutant behavior to cluster the mutants so that the ones with similar behavior fall into the same group. A representative from each group is then selected for testing, and the result of the test, e.g., whether the mutant is killed or survived, is reused for all other mutants represented by the selected mutant, obviating the need for testing other mutants. 14 DNN models of sizes ranging from thousands to millions of parameters, trained on different datasets, are used to evaluate DM# and compare it to several baseline techniques. Our results provide empirical evidence on the effectiveness of DM# in accelerating mutation testing by 28.38%, on average, at the average cost of only 0.72% error in mutation score. Moreover, on average, DM# incurs 11.78, 15.16, and 114.36 times less mutation score error compared to random mutant selection, boundary sample selection, and random sample selection techniques, respectively, while generally offering comparable speed-up.