The cohesin ring, which is composed of the Smc1, Smc3, and Scc1 subunits, topologically embraces two sister chromatids from S phase until anaphase to ensure their precise segregation to the daughter cells. The opening of the ring is required for its loading on the chromosomes and unloading by the action of Wpl1 protein. Both loading and unloading are dependent on ATP hydrolysis by the Smc1 and Smc3 "head" domains, which engage to form two composite ATPase sites. Based on the available structures, we modeled the Saccharomyces cerevisiae Smc1/Smc3 head heterodimer and discovered that the Smc1/Smc3 interfaces at the two ATPase sites differ in the extent of protein contacts and stability after ATP hydrolysis. We identified smc1 and smc3 mutations that disrupt one of the interfaces and block the Wpl1-mediated release of cohesin from DNA. Thus, we provide structural insights into how the cohesin heads engage with each other.