Mutations in proteins like FUS which cause Amyotrophic Lateral Sclerosis (ALS) result in the aberrant formation of stress granules while ALS-linked mutations in other proteins impede elimination of stress granules. Repeat expansions in C9ORF72, the major cause of ALS, reduce C9ORF72 levels but how this impacts stress granules is uncertain. Here, we demonstrate that C9ORF72 associates with the autophagy receptor p62 and controls elimination of stress granules by autophagy. This requires p62 to associate via the Tudor protein SMN with proteins, including FUS, that are symmetrically methylated on arginines. Mice lacking p62 accumulate arginine-methylated proteins and alterations in FUS-dependent splicing. Patients with C9ORF72 repeat expansions accumulate symmetric arginine dimethylated proteins which co-localize with p62. This suggests that C9ORF72 initiates a cascade of ALS-linked proteins (C9ORF72, p62, SMN, FUS) to recognize stress granules for degradation by autophagy and hallmarks of a defect in this process are observable in ALS patients.