Genome sizes have evolved to vary widely, from 250 bases in viroids to 670 billion bases in some amoebas. This remarkable variation in genome size is the outcome of complex interactions between various evolutionary factors such as mutation rate and population size. While comparative genomics has uncovered how some of these evolutionary factors influence genome size, we still do not understand what drives genome size evolution. Specifically, it is not clear how the primordial mutational processes of base substitutions, insertions, and deletions influence genome size evolution in asexual organisms. Here, we use digital evolution to investigate genome size evolution by tracking genome edits and their fitness effects in real time. In agreement with empirical data, we find that mutation rate is inversely correlated with genome size in asexual populations. We show that at low point mutation rate, insertions are significantly more beneficial than deletions, driving genome expansion and the acquisition of phenotypic complexity. Conversely, the high mutational load experienced at high mutation rates inhibits genome growth, forcing the genomes to compress their genetic information. Our analyses suggest that the inverse relationship between mutation rate and genome size is a result of the tradeoff between evolving phenotypic innovation and limiting the mutational load.