Clarifying the optimal combination of N fertilizer application rate and application method can maximize the yield of drip-irrigated sugar beet in arid areas, which is of great significance for reducing farmland N pollution and achieving sustainable agricultural development. In this three-year field experiment in Xinjiang, China, the effects of three N application rates [75 kg ha−1 (N1), 150 kg ha−1 (N2), and 225 kg ha−1 (N3)] and three N application methods [the proportion of N applied at canopy rapid growth stage, taproot expansion stage, and sugar accumulation stage were (M1) 100%: 0%: 0%, (M2) 70%: 30%: 0%, and (M3) 50%: 30%: 20%] on the dry matter accumulation (DMA) and distribution, leaf senescence, yield, and agronomic N use efficiency (aNUE) of drip-irrigated sugar beet were explored. The results showed that N application (N1, N2, and N3 treatments) increased the shoot DMA by 27.7% (three-year average), 52.6%, and 83.1%, and the taproot DMA by 28.3%, 43.2%, and 61.6%, respectively (p < 0.05), compared with CK (no N supply) treatment. The N application methods M2 and M3 increased the shoot DMA by 5.6% (three-year average) and 1.0% (p > 0.05), respectively, and the taproot DMA by 7.2% and 3.6% (p < 0.05), respectively, compared with M1. In addition, M2 could delay the end of shoot and taproot growth (te) and the occurrence of maximum growth rate (tm). In particular, the N3M2 treatment increased the leaf area index (LAI) by 20.4–75.9% (p < 0.05) compared with other treatments by increasing the leaf area duration (LAD) and decreasing the leaf senescence rate (LSR). The taproot yield and sugar yield of N3M2 treatment reached the maximum at harvest time, but there was no significant difference in taproot yield and sugar yield between N3M2 treatment and N2M2 treatment. The aNUE in N2M2 treatment was the highest (p < 0.05), which was 1.29–7.85 times higher than that of other treatments. Therefore, reducing the N application rate from 225 kg·ha−1 to 150 kg·ha−1 and applying 70% and 30% of 150 kg N ha−1 at the canopy rapid growth stage and the taproot expansion stage, respectively, could achieve the goal of increasing sugar beet yield and N use efficiency. This study will provide an important reference for the sustainable production of sugar beet under drip irrigation in Xinjiang, China.