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Abstract Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the δ‐adjusted and control‐based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets a broad class of treatment effect estimands defined as functionals of treatment‐specific survival functions, taking into account missing data due to censoring. Multiple imputation facilitates the use of simple full‐sample estimation; however, the standard Rubin's combining rule may overestimate the variance for inference in the sensitivity analysis framework. We decompose the multiple imputation estimator into a martingale series based on the sequential construction of the estimator and propose the wild bootstrap inference by resampling the martingale series. The new bootstrap inference has a theoretical guarantee for consistency and is computationally efficient compared to the nonparametric bootstrap counterpart. We evaluate the finite‐sample performance of the proposed SMIM through simulation and an application on an HIV clinical trial.