Minichromosome maintenance protein 10 (MCM10) is essential for eukaryotic DNA replication. Here, we describe compound heterozygous MCM10 variants in patients with distinctive, but overlapping, clinical phenotypes: natural killer (NK) cell deficiency (NKD) and restrictive cardiomyopathy (RCM) with hypoplasia of the spleen and thymus. To understand the mechanism of MCM10-associated disease, we modeled these variants in human cell lines. MCM10 deficiency causes chronic replication stress that reduces cell viability due to increased genomic instability and telomere erosion. Our data suggest that loss of MCM10 function constrains telomerase activity by accumulating abnormal replication fork structures enriched with single-stranded DNA. Terminally-arrested replication forks in MCM10-deficient cells require endonucleolytic processing by MUS81, as MCM10:MUS81 double mutants display decreased viability and accelerated telomere shortening. We propose that these bi-allelic variants in MCM10 predispose specific cardiac and immune cell lineages to prematurely arrest during differentiation, causing the clinical phenotypes observed in both NKD and RCM patients.