Since the relationship of mortality-temperature is nonlinear, takes U or V shape, and cannot be expressed by a parametric model, in this article, a semiparametric spatial mixed effects model is proposed to simultaneously identify the non-linear relationship and detect spatial change points after adjusting for some explanatory weather variables. An algorithm is proposed for model estimation and spatial change points detection simultaneously. In addition, a permutation test is introduced to test the significance of detected change points. Various simulation studies are conducted to evaluate the performance of our approach in two cases (1) when there is a common change point, and (2) there are different change points over locations. The advantages of our proposed model and its estimation algorithm are demonstrated using epidemiology data on mortality and temperature and other weather variables in six major cities in South Korea.