Tackling unsupervised source separation jointly with an additional inverse problem such as deconvolution is central for the analysis of multi-wavelength data. This becomes highly challenging when applied to large data sampled on the sphere such as those provided by wide-field observations in astrophysics, whose analysis requires the design of dedicated robust and yet effective algorithms. We therefore investigate a new joint deconvolution/sparse blind source separation method dedicated for data sampled on the sphere, coined SDecGMCA. It is based on a projected alternate least-squares minimization scheme, whose accuracy is proved to strongly rely on some regularization scheme in the present joint deconvolution/blind source separation setting. To this end, a regularization strategy is introduced that allows designing a new robust and effective algorithm, which is key to analyze large spherical data. Numerical experiments are carried out on toy examples and realistic astronomical data.