Mindfulness training is associated with improvements in psychological wellbeing and cognition, yet the specific underlying neurophysiological mechanisms underpinning these changes are uncertain. This study uses a novel brain-inspired artificial neural network to investigate the effect of mindfulness training on electroencephalographic function. Participants completed a 4-tone auditory oddball task (that included targets and physically similar distractors) at three assessment time points. In Group A (n = 10), these tasks were given immediately prior to 6-week mindfulness training, immediately after training and at a 3-week follow-up; in Group B (n = 10), these were during an intervention waitlist period (3 weeks prior to training), pre-mindfulness training and post-mindfulness training. Using a spiking neural network (SNN) model, we evaluated concurrent neural patterns generated across space and time from features of electroencephalographic data capturing the neural dynamics associated with the event-related potential (ERP). This technique capitalises on the temporal dynamics of the shifts in polarity throughout the ERP and spatially across electrodes. Findings support anteriorisation of connection weights in response to distractors relative to target stimuli. Right frontal connection weights to distractors were associated with trait mindfulness (positively) and depression (inversely). Moreover, mindfulness training was associated with an increase in connection weights to targets (bilateral frontal, left frontocentral, and temporal regions only) and distractors. SNN models were superior to other machine learning methods in the classification of brain states as a function of mindfulness training. Findings suggest SNN models can provide useful information that differentiates brain states based on distinct task demands and stimuli, as well as changes in brain states as a function of psychological intervention.