Plants can adapt to the spatial heterogeneity of soil nutrients by changing the morphology and architecture of the root system. Here, we explored the role of auxin in the response of sweetpotato roots to potassium (K+) deficiency stress. Two sweetpotato cultivars, Xushu 32 (low-K-tolerant) and Ningzishu 1 (low-K-sensitive), were cultured in low K+(0.1 mmol L−1, LK) and normal K+(10 mmol L−1, CK) nutrient solutions. Compared with CK, LK reduced the dry mass, K+content, and K+accumulation in the two cultivars, but the losses of Xushu 32 were smaller than those of Ningzishu 1. LK also affected root growth, mainly impairing the length, surface area, forks number, and crossings number. However, Xushu 32 had significantly higher lateral root length, density, and surface area than Ningzishu 1, closely related to the roots’ higher indole-3-acetic acid (IAA) content. According to the qPCR results, Xushu 32 synthesized more IAA (viaIbYUC8andIbTAR2) in leaves but transported and accumulated in roots through polar transport (viaIbPIN1,IbPIN3, andIbAUX1). It was also associated with the upregulation of auxin signaling pathway genes (IbIAA4andIbIAA8) in roots. These results imply that IAA participates in the formation of lateral roots and the change in root architecture during the tolerance to low K+stress of sweetpotato, thus improving the absorption of K+and the formation of biomass.