Many studies in nonlinear science heavily rely on surrogate-based hypothesis testing to provide significance estimations of analysis results. Among the complex data produced by nonlinear systems, spike trains are a class of sequences requiring algorithms for surrogate generation that are typically more sophisticated and computationally demanding than methods developed for continuous signals. Although algorithms to specifically generate surrogate spike trains exist, the availability of open-source, portable implementations is still incomplete. In this paper, we introduce the SpiSeMe (Spike Sequence Mime) software package that implements four algorithms for the generation of surrogate data out of spike trains and more generally out of any sequence of discrete events. The purpose of the package is to provide a unified and portable toolbox to carry out surrogate generation on point-process data. Code is provided in three languages, namely, C++, Matlab, and Python, thus allowing straightforward integration of package functions into most analysis pipelines.