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Dynamic security assessment (DSA) is a critical function to evaluate power grids' capability to survive the transition caused by a set of disturbances to an acceptable steady-state condition. Its computational burden is heavy. With the challenges brought by renewable energy and new smart grid technologies, DSA under uncertainty has to be considered to study the impact of forecast errors on DSA simulation, which further increases the computational burden. To address this challenge, this paper presents a high performance computational framework to support DSA simulation user uncertainty. The computational framework provides a seamless work flow that links data from high performance computing, statistical analysis, to visualization so that a problem can be easily expressed in a way compatible with different functions. It also enables software compatibility such that application development can be more efficient. Case study results of the ESCA60 system and a western U.S. system show the advantages and efficiency of the computational framework.