Noncoding RNAs are exquisitely titrated by the cellular RNA surveillance machinery for regulating diverse biological processes. The RNA exosome, the predominant 3′ RNA exoribonuclease in mammalian cells, is composed of nine core and two catalytic subunits. Here, we developed a mouse model with a conditional allele to study the RNA exosome catalytic subunit DIS3. In DIS3-deficient B cells, integrity of the immunoglobulin heavy chain (Igh) locus in its topologically associating domain is affected, with accumulation of DNA-associated RNAs flanking CTCF-binding elements, decreased CTCF binding to CTCF-binding elements and disorganized cohesin localization. DIS3-deficient B cells also accumulate activation-induced cytidine deaminase–mediated asymmetric nicks, altering somatic hypermutation patterns and increasing microhomology-mediated end-joining DNA repair. Altered mutation patterns and Igh architectural defects in DIS3-deficient B cells lead to decreased class-switch recombination but increased chromosomal translocations. Our observations of DIS3-mediated architectural regulation at the Igh locus are reflected genome wide, thus providing evidence that noncoding RNA processing is an important mechanism for controlling genome organization.