The cohesin complex is essential for sister chromatid cohesion during mitosis. Its Smc1 and Smc3 subunits are rod-shaped molecules with globular ABC-like ATPases at one end and dimerization domains at the other connected by long coiled coils. Smc1 and Smc3 associate to form V-shaped heterodimers. Their ATPase heads are thought to be bridged by a third subunit, Scc1, creating a huge triangular ring that could trap sister DNA molecules. We address here whether cohesin forms such rings in vivo. Proteolytic cleavage of Scc1 by separase at the onset of anaphase triggers its dissociation from chromosomes. We show that N- and C-terminal Scc1 cleavage fragments remain connected due to their association with different heads of a single Smc1/Smc3 heterodimer. Cleavage of the Smc3 coiled coil is sufficient to trigger cohesin release from chromosomes and loss of sister cohesion, consistent with a topological association with chromatin.