Tuber crops cultivated in basalt-derived soils are influenced by naturally high geochemical backgrounds, which may elevate heavy metal(loid) levels and associated health risks. To clarify the geochemical controls governing metal accumulation, this study analyzed rock, soil, and tuber (sweet potato and yam) samples from the Qiongbei volcanic area of Hainan Island, China. Concentrations of eight heavy metal(loid)s (As, Cd, Cr, Cu, Hg, Ni, Pb, and Zn) and 22 nutrient-related indicators (N, P, K, SOC, S, Se, Fe, Mn, and their available fractions) were determined. Soil contamination and potential human health risks were evaluated using the pollution index and the health risk model. The results showed that 11.1–55.6% of soil samples exceeded pollution thresholds for Cr, Cu, Ni, and Zn, reflecting typical basaltic high-background characteristics. In contrast, heavy metal(loid) concentrations in tuber crops were relatively low and jointly regulated by parent material composition and soil nutrient status. Non-carcinogenic risks (HI) were below 1, indicating acceptable exposure levels, while carcinogenic risks were mainly associated with Cd, Cr, and Pb, with total carcinogenic risk (TCR) exceeding 1 × 10⁻⁴, suggesting potential health concerns. Strong correlations between soil nutrients (N, P, K, SOC, S, Se, Mn, and Fe) and plant uptake of As, Cd, Cu, and Cr indicate that nutrient availability plays a crucial role in controlling heavy metal(loid) bioavailability. The volcanic soils exhibited a “high total content–low bioavailability” pattern. Enhancing soil Se, SOC, available N, and slowly available K (SAK) can effectively reduce Cd and other high-risk metal accumulation in tuber crops. These findings elucidate the key geochemical processes influencing heavy metal transfer in volcanic agroecosystems and provide a scientific basis for safe agricultural utilization and health risk prevention in high-background regions.