AbstractSeparating different sources of signal in Interferometric Synthetic Aperture Radar (InSAR) studies over large areas is challenging, especially between the long‐wavelength changes of atmospheric conditions and tectonic deformations, both correlated to elevation. In this study, we focus on the 2017–2018 slow slip event (SSE) in the Guerrero state (Mexico) where (1) the permanent GPS network has a low spatial density (less than 30 stations in an area of 300  300 km) with uneven distribution; (2) the tropospheric phase delays can be as high as 20 cm of apparent ground displacements, with a complex temporal evolution; (3) the tested global weather models fail to correct interferograms with enough accuracy (with residual tropospheric signal higher than the tectonic signal); and (4) the surface displacement caused by the seismic cycle shows complex interactions between seismic sequences and aseismic events. To extract the SSE signal from Sentinel‐1 InSAR time series, we test two different approaches. The first (parametric method) consists of a least squares linear inversion, imposing a functional form for each deformation or atmospheric component. The second uses independent component analysis of the InSAR time series. We obtain time series maps of surface displacements along the radar line of sight associated with the SSE and validate these results with a comparison to GPS. Combining those two approaches, we propose a method to separate atmospheric delays and tectonic deformation on time series data not corrected from atmospheric delays. From the extracted ground deformation maps, we propose a first‐order slip inversion model at the subduction interface during this SSE.