In this study we present microstructural data from hydrothermal veins in the sedimentary cover and the igneous basement recovered from Hole U1414A, Integrated Ocean Drilling Program (IODP) Expedition 344 (Costa Rica Seismogenesis Project), to constrain deformation mechanism operating in the subducting Cocos Plate. Cathodoluminescence studies, mechanical e‐twin piezometry and electron backscatter diffraction (EBSD) analyses of carbonate veins were used to give insights into the deformation conditions and to help to understand the tectonic deformation history of the Cocos Plate offshore Costa Rica. Analyses of microstructures in the sedimentary rocks and in the basalt of the igneous basement reveal brittle deformation, as well as crystal‐plastic deformation of the host rock and the vein material. Cathodoluminescence images showed that in the basalt fluid flow and related precipitation occurred over several episodes. The differential stresses, obtained from two different piezometers using the same parameter (twin density), indicate various mean differential stresses of 49 ± 11 and 69 ± 30 MPa and EBSD mapping of calcite veins reveals low‐angle subgrain boundaries. Deformation temperatures are restricted to the range from 170°C to 220°C, due to the characteristics of the existing twins and the lack of high‐temperature intracrystalline deformation mechanisms (>220°C). The obtained results suggest that deformation occurred over a period associated with changes of ambient temperatures, occurrence of fluids and hydrofracturing, induced differential stresses due to the bending of the plate at the trench, and related seismic activity.