Propagation of viruses requires interaction with host factors in infected cells and repression of innate immune responses triggered by the host viral sensors. Cytosolic DNA sensing pathway of cyclic GMP-AMP synthase (cGAS) and stimulator of interferon genes (STING) is a major component of the antiviral response to DNA viruses, also known to play a relevant role in response to infection by RNA viruses, including foot-and-mouth disease virus (FMDV). Here, we provide supporting evidence of cGAS degradation in swine cells during FMDV infection and show that the two virally encoded proteases, Leader (Lpro) and 3Cpro, target cGAS for cleavage to dampen the cGAS/STING-dependent antiviral response. The specific target sequence sites on swine cGAS were identified as Q140/T141 for the FMDV 3Cpro and the KVKNNLKRQ motif at residues 322–330 for Lpro. Treatment of swine cells with inhibitors of the cGAS/STING pathway or depletion of cGAS promoted viral infection, while overexpression of a mutant cGAS defective for cGAMP synthesis, unlike wild type cGAS, failed to reduce FMDV replication. Our findings reveal a new mechanism of RNA viral antagonism of the cGAS-STING innate immune sensing pathway, based on the redundant degradation of cGAS through the concomitant proteolytic activities of two proteases encoded by an RNA virus, further proving the key role of cGAS in restricting FMDV infection.