This paper introduces a new methodology for dynamic learning, visualization, and classification of functional magnetic resonance imaging (fMRI) as spatiotemporal brain data. The method is based on an evolving spatiotemporal data machine of evolving spiking neural networks (SNNs) exemplified by the NeuCube architecture [1]. The method consists of several steps: mapping spatial coordinates of fMRI data into a 3-D SNN cube (SNNc) that represents a brain template; input data transformation into trains of spikes; deep, unsupervised learning in the 3-D SNNc of spatiotemporal patterns from data; supervised learning in an evolving SNN classifier; parameter optimization; and 3-D visualization and model interpretation. Two benchmark case study problems and data are used to illustrate the proposed methodology-fMRI data collected from subjects when reading affirmative or negative sentences and another one-on reading a sentence or seeing a picture. The learned connections in the SNNc represent dynamic spatiotemporal relationships derived from the fMRI data. They can reveal new information about the brain functions under different conditions. The proposed methodology allows for the first time to analyze dynamic functional and structural connectivity of a learned SNN model from fMRI data. This can be used for a better understanding of brain activities and also for online generation of appropriate neurofeedback to subjects for improved brain functions. For example, in this paper, tracing the 3-D SNN model connectivity enabled us for the first time to capture prominent brain functional pathways evoked in language comprehension. We found stronger spatiotemporal interaction between left dorsolateral prefrontal cortex and left temporal while reading a negated sentence. This observation is obviously distinguishable from the patterns generated by either reading affirmative sentences or seeing pictures. The proposed NeuCube-based methodology offers also a superior classification accuracy when compared with traditional AI and statistical methods. The created NeuCube-based models of fMRI data are directly and efficiently implementable on high performance and low energy consumption neuromorphic platforms for real-time applications.