A long-standing evolutionary puzzle is that all eukaryotic genomes contain large amounts of tandemly-repeated DNA whose sequence motifs and abundance vary greatly among even closely related species. To elucidate the evolutionary forces governing tandem repeat dynamics, quantification of the rates and patterns of mutations in repeat copy number and tests of its selective neutrality are necessary. Here, we used whole-genome sequences of 28 mutation accumulation (MA) lines of Daphnia pulex, in addition to six isolates from a non-MA population originating from the same progenitor, to both estimate mutation rates of abundances of repeat sequences and evaluate the selective regime acting upon them. We found that mutation rates of individual repeats were both high and highly variable, ranging from additions/deletions of 0.29-105 copies per generation (reflecting changes of 0.12-0.80% per generation). Our results also provide evidence that new repeat sequences are often formed from existing ones. The non-MA population isolates showed a signal of either purifying or stabilizing selection, with 33% lower variation in repeat copy number on average than the MA lines, although the level of selective constraint was not evenly distributed across all repeats. The changes between many pairs of repeats were correlated, and the pattern of correlations was significantly different between the MA lines and the non-MA population. Our study demonstrates that tandem repeats can experience extremely rapid evolution in copy number, which can lead to high levels of divergence in genome-wide repeat composition between closely related species.