Sweet potato is a tuberous root crop with strong environmental stress resistance. It is beneficial to study its storage root formation and stress responses to identify sweet potato stress- and storage-root-thickening-related regulators. Here, six conserved miRNAs (miR156g, miR157d, miR158a-3p, miR161.1, miR167d and miR397a) and six novel miRNAs (novel 104, novel 120, novel 140, novel 214, novel 359 and novel 522) were isolated and characterized in sweet potato. Tissue-specific expression patterns suggested that miR156g, miR157d, miR158a-3p, miR167d, novel 359 and novel 522 exhibited high expression in fibrous roots or storage roots and were all upregulated in response to storage-root-related hormones (indole acetic acid, IAA; zeaxanthin, ZT; abscisic acid, ABA; and gibberellin, GAs). The expression of miR156g, miR158a-3p, miR167d, novel 120 and novel 214 was induced or reduced dramatically by salt, dehydration and cold or heat stresses. Moreover, these miRNAs were all upregulated by ABA, a crucial hormone modulator in regulating abiotic stresses. Additionally, the potential targets of the twelve miRNAs were predicted and analyzed. Above all, these results indicated that these miRNAs might play roles in storage root development and/or stress responses in sweet potato as well as provided valuable information for the further investigation of the roles of miRNA in storage root development and stress responses.