In Amyotrophic Lateral Sclerosis (ALS) motor neuron disease, mutations in proteins that upon stress localize within cytoplasmic protein inclusions called Stress Granules (SGs), are linked to the formation of aberrant inclusions, which are related to neuronal cell death. By combining studies in human cells and C. elegans including the use of Nanobodies, we found that inhibition of NEDP1, the enzyme responsible for the processing and deconjugation of the Ubiquitin-like molecule NEDD8 from substrates, promotes the elimination both of physiological and pathological SGs. The hyper-NEDDylation of Poly-(ADP-ribose) polymerase-1 enzyme upon NEDP1 inhibition compromises PAR production and is a key mechanism for the observed SG phenotype. Importantly, the above-described effects are related to improved cell survival in human cells, and in C. elegans, NEDP1 deletion ameliorates ALS-phenotypes related to animal motility. Our studies reveal NEDP1 as potential therapeutic target for ALS, based on the elimination of aberrant SGs.