As an erosion dynamic index considering the three elements of flood, runoff erosion power (REP) can better reflect the influence of precipitation, underlying surface, and other factors on the erosion and sediment transport (ST) of flood events. Therefore, it is of great significance to study the variation characteristics of the REP and its relationship with ST in the basin for soil erosion control. In this paper, the Fujiang River Basin (FRB) was selected to analyze the characteristics of runoff and ST at four hydrological stations in the basin from 2009 to 2018, including Santai, Jiangyou, Shehong, and Xiaoheba. Combined with the concept of the REP, six kinds of water–sediment relationship were compared and analyzed. Furthermore, by constructing the SWAT model, the spatial distribution characteristics of runoff, ST, and REP in the FRB were analyzed in depth, and the spatial scale effect of the REP in the basin was explored. The conclusions are as follows: (1) The power function relationship between REP and sediment transport modulus (STM) is better than the other five kinds of water–sediment relationship. (2) Based on the SWAT model, the evaluation indexes of the monthly runoff and ST of the four hydrological stations are credible, good, and excellent in the rating period (RP) and the validation period (VP). (3) The annual REP in the main stream from upstream to downstream is mostly a single change trend, while in each primary tributary, the overall value is larger than that of the main stream and the interannual difference is obvious. The average annual REP generally shows the distribution characteristics of ‘large at the junction of the upper and middle reaches and small in the rest of the area’. With the increase in the control area, the multi-year average REP has a decreasing trend, especially when the catchment area above the sub-watershed is >7318 km2; the change of the multi-year average REP is single and obviously slows down, with an average value of 23.8 mm·m3·s−1·km−2.