The joint contribution of pre-existing and de novo genetic variation to clonal adaptation is poorly understood but essential to designing successful antimicrobial or cancer therapies. To address this, we evolve genetically diverse populations of budding yeast, S. cerevisiae, consisting of diploid cells with unique haplotype combinations. We study the asexual evolution of these populations under selective inhibition with chemotherapeutic drugs by time-resolved whole-genome sequencing and phenotyping. All populations undergo clonal expansions driven by de novo mutations but remain genetically and phenotypically diverse. The clones exhibit widespread genomic instability, rendering recessive de novo mutations homozygous and refining pre-existing variation. Finally, we decompose the fitness contributions of pre-existing and de novo mutations by creating a large recombinant library of adaptive mutations in an ensemble of genetic backgrounds. Both pre-existing and de novo mutations substantially contribute to fitness, and the relative fitness of pre-existing variants sets a selective threshold for new adaptive mutations.