Multivariate spatial count data are often segmented by unobserved space‐varying factors that vary across space. In this setting, regression models that assume space‐constant covariate effects could be too restrictive. Motivated by the analysis of cause‐specific mortality data, we propose to estimate space‐varying effects by exploiting a multivariate hidden Markov field. It models the data by a battery of Poisson regressions with spatially correlated regression coefficients, which are driven by an unobserved spatial multinomial process. It parsimoniously describes multivariate count data by means of a finite number of latent classes. Parameter estimation is carried out by composite likelihood methods, that we specifically develop for the proposed model. In a case study of cause‐specific mortality data in Italy, the model was capable to capture the spatial variation of gender differences and age effects.