The resolution of recombination intermediates containing Holliday junctions (HJs) is critical for genome maintenance and proper chromosome segregation. Three pathways for HJ processing exist in human cells and involve the following enzymes/complexes: BLM-TopoIIIα-RMI1-RMI2 (BTR complex), SLX1-SLX4-MUS81-EME1 (SLX-MUS complex), and GEN1. Cycling cells preferentially use the BTR complex for the removal of double HJs in S phase, with SLX-MUS and GEN1 acting at temporally distinct phases of the cell cycle. Cells lacking SLX-MUS and GEN1 exhibit chromosome missegregation, micronucleus formation, and elevated levels of 53BP1-positive G1 nuclear bodies, suggesting that defects in chromosome segregation lead to the transmission of extensive DNA damage to daughter cells. In addition, however, we found that the effects of SLX4, MUS81, and GEN1 depletion extend beyond mitosis, since genome instability is observed throughout all phases of the cell cycle. This is exemplified in the form of impaired replication fork movement and S-phase progression, endogenous checkpoint activation, chromosome segmentation, and multinucleation. In contrast to SLX4, SLX1, the nuclease subunit of the SLX1-SLX4 structure-selective nuclease, plays no role in the replication-related phenotypes associated with SLX4/MUS81 and GEN1 depletion. These observations demonstrate that the SLX1-SLX4 nuclease and the SLX4 scaffold play divergent roles in the maintenance of genome integrity in human cells.