We analyze the strong hexagonal warping of the Dirac cone of Bi2Te3 by angle- resolved photoemission. Along Γ¯¯¯M¯¯¯, the dispersion deviates from a linear behavior meaning that the Dirac cone is warped outwards and not inwards. We show that this introduces an anisotropy in the lifetime broadening of the topological surface state which is larger along Γ¯¯¯K¯¯¯. The result is not consistent with an explanation by nesting properties. Based on the theoretically predicted modifications of the ground-state spin texture of a strongly warped Dirac cone, we propose spin-dependent scattering processes as explanation for the anisotropic scattering rates. These results could help paving the way for optimizing future spintronic devices using topological insulators and controlling surface-scattering processes via external gate voltages.