Sweet potato (Ipomoea batatas) ranks among the most important crops in the world and provides nutritional and economic sustainability for subsistence farmers in sub-Saharan Africa. Its production is mainly constrained by sweet potato virus disease (SPVD) caused by the coinfection of two positive-sense single-stranded RNA viruses, sweet potato chlorotic stunt virus (SPCSV) and sweet potato feathery mottle virus (SPFMV). Current understanding of sweet potato responses to SPCSV and SPFMV at the molecular level remains very limited. In this study, we performed deep sequencing of both messenger RNA (mRNA) and small RNA (sRNA) populations in an SPVD-susceptible cultivar ‘Beauregard’ upon viral infection, to identify biological pathways that contribute to both general and specific host responses to these important viral pathogens. We found that pathways related to stress response and signaling were significantly affected by viral infection. sRNA components of these pathways were predominantly affected in late stages of the coinfection by SPCSV and SPFMV. We identified several novel microRNAs that were responsive to viral infection, some of which were predicted to target nucleotide-binding site leucine-rich repeat (NBS-LRR) disease resistance genes. The downregulation of the salicylic acid-mediated defense response pathway in particular seems to be a result of the viral infection process, and can in part explain the susceptible nature of the ‘Beauregard’ cultivar.