In this article, we present the R package mutualinf for computing and decomposing the mutual information index of segregation by means of recursion and parallelization techniques. The mutual information index is the only multigroup index of segregation that satisfies strong decomposability properties, both for organizational units and groups. The mutualinf package contributes by (1) implementing the decomposition of the mutual information index into a "between" and a "within" term; (2) computing, in a single call, a chain of decompositions that involve one "between" term and several "within" terms; (3) providing the contributions of the variables that define the groups or the organizational units to the overall segregation; and (4) providing the demographic weights and local indexes employed in the computation of the "within" term. We illustrate the use of mutualinf using Chilean school enrollment data. With these data, we study socioeconomic and ethnic segregation in schools.