Behavioral states in humans and animals vary over time, and these shifts alter cortical processing and cognitive function. For example, one striking result is an observed inverted-U relationship between arousal and performance on signal detection tasks. However, there is currently a need for mechanistic models that can explain these state-dependent effects. Here we address this challenge in the context of arousal-dependent auditory processing in rodents. In experiments where mice were presented tones of different frequencies, we found that frequency information could be best decoded from population activity during states of moderate arousal, compared to either low or high arousal. We explain the computational mechanism of this optimal stimulus processing with a spiking network model composed of excitatory and inhibitory cells arranged in clusters. Neural activity in this circuit unfolds through metastable attractors representing transiently activated neural assemblies. By modeling varying arousal levels as perturbations to excitatory cells’ baseline external inputs, we show that increasing input heterogeneity modulates stimulus decoding in a manner consistent with the data. That is, intermediate levels of heterogeneity – modeling intermediate arousals – yield optimal discriminability. Moreover, comparison to a model with homogeneous architecture reveals that clustered organization is necessary to explain the observed inverted-U relationship between decoding performance and arousal. Using mean-field theory, we then show that variations in stimulus decoding arise due to a perturbation- (i.e, arousal-) induced shift in the dynamical regime of the circuit. Increasing arousal in the model from low to moderate levels accelerates the network’s metastable dynamics, leading to an optimal coding regime. But at high arousals, metastable dynamics disappear and decoding performance degrades, explaining the empirical results. Beyond the current application, the framework we present can be extended to understand context-dependent neural computation more broadly. For example, it could be utilized to study pharmacologically- or optogenetically-induced shifts in cortical state.