Deep neural networks perform very well in learning high-level representations in support of multivariate geochemical anomaly recognition. Geochemical exploration data typically contain a proportion of large variations and missing values, which motivated us to construct a network architecture optimized to deal with these data. Our approach adopted a stacked convolutional denoising autoencoder (SCDAE) to extract robust features and decreased the level of sensitivity to partially corrupted data, that is, input data that are partially missing. SCDAE parameters, which include the network depth, number of convolution layers, number of convolution kernels, and convolution kernel size, were optimized using trial-and-error experiments. The optimal SCDAE architecture was then used to recognize multivariate geochemical anomalies related to mineralization in a case study in southwestern Fujian Province, based on the differences in the reconstruction errors between sample populations. The spatial distribution of high reconstruction errors in the anomaly map was closely related to most known Fe deposits, indicating the effectiveness of the SCDAE at recognizing geochemical anomalies related to Fe mineralization. A comparative study between the SCDAE and a stacked convolutional autoencoder (SCAE) with different corruption levels showed that the SCDAE exhibited reduced sensitivity to stochastic disturbances with different corruption proportions, and had an enhanced ability to recognize geochemical anomalies varying in a reasonable range. The robustness of the SCDAE makes it applicable to a wide variety of geochemical exploration scenarios, particularly in areas with incomplete or missing data.