Background: Response to neoadjuvant chemotherapy (NACT) has been proven to be an established prognostic factor after open radical cystectomy (ORC). We evaluated the impact of NACT on survival outcomes of a single-institution robotic radical cystectomy (RARC) series. Methods: From January 2012 to June 2020, 79 patients were identified. Baseline, demographic, perioperative, and pathologic data were described. Kaplan–Meier with the log-rank test was used to compare overall survival (OS) differences between complete, partial, and no-NACT responders, respectively. Univariable and multivariable regression analyses were performed to identify predictors of OS. Results: Complete, partial, and absent response to NACT were recorded in 43 (54.4%), 21 (19%), and 15 (26.6%) patients, respectively. A complete response to NACT displayed a trend toward significant higher OS (p = 0.03). In univariable analysis, significant predictors of lower OS were hypertension (HR 3.37; CI 95% 1.31–8.62; p = 0.01); advanced nodal involvement (HR 2.41; CI 95% 0.53–10.9; p < 0.001); and incomplete response to NACT (HR 0.41; CI 95% 0.18–0.95; p = 0.039). In multivariable analysis, the only independent predictor of worse OS was advanced pathologic N stages (HR 10.1; CI: 95% CI 2.3–44.3; p = 0.002). Conclusions: Complete response to NACT is associated with increased OS probability, but significant nodal residual disease remains the only independent predictor of OS after RARC.