A developmental disorder that severely damages communicative and social functions, the Autism Spectrum Disorder (ASD) also presents aspects related to mental rigidity, repetitive behavior, and difficulty in abstract reasoning. More, imbalances between excitatory and inhibitory brain states, in addition to cortical connectivity disruptions, are at the source of the autistic behavior. Our main goal consists in unveiling the way by which these local excitatory imbalances and/or long brain connections disruptions are linked to the above mentioned cognitive features. We developed a theoretical model based on Self-Organizing Maps (SOM), where a three-level artificial neural network qualitatively incorporates these kinds of alterations observed in brains of patients with ASD. Computational simulations of our model indicate that high excitatory states or long distance under-connectivity are at the origins of cognitive alterations, as difficulty in categorization and mental rigidity. More specifically, the enlargement of excitatory synaptic reach areas in a cortical map development conducts to low categorization (over-selectivity) and poor concepts formation. And, both the over-strengthening of local excitatory synapses and the long distance under-connectivity, although through distinct mechanisms, contribute to impaired categorization (under-selectivity) and mental rigidity. Our results indicate how, together, both local and global brain connectivity alterations give rise to spoiled cortical structures in distinct ways and in distinct cortical areas. These alterations would disrupt the codification of sensory stimuli, the representation of concepts and, thus, the process of categorization - by this way imposing serious limits to the mental flexibility and to the capacity of generalization in the autistic reasoning.