We apply the optimal filter technique to Sloan Digital Sky Survey photometry around Segue 1 and find that the outer parts of the cluster are distorted. There is strong evidence for ~ 1 degree elongations of extra-tidal stars, extending both eastwards and southwestwards of the cluster. The extensions have similar differential Hess diagrams to Segue 1. A Kolmogorov-Smirnov test suggests a high probability that both come from the same parent distribution. The location of Segue 1 is close to crossings of the tidal wraps of the Sagittarius stream. By extracting blue horizontal branch stars from Sloans spectral database, two kinematic features are isolated and identified with different wraps of the Sagittarius stream. We show that Segue 1 is moving with a velocity that is close to one of the wraps. At this location, we estimate that there are enough Sagittarius stars, indistinguishable from Segue 1 stars, to inflate the velocity dispersion and hence the mass-to-light ratio. All the available evidence is consistent with the interpretation that Segue 1 is a star cluster, originally from the Sagittarius galaxy, and now dissolving in the Milky Way.