Singularity behaviour in circadian clocks--the loss of robust circadian rhythms following exposure to a stimulus such as a pulse of bright light--is one of the fundamental but mysterious properties of clocks. To quantitatively perturb and accurately measure the dynamics of cellular clocks, we synthetically produced photo-responsiveness within mammalian cells by exogenously introducing the photoreceptor melanopsin and continuously monitoring the effect of photo-perturbation on the state of cellular clocks. Here we report that a critical light pulse drives cellular clocks into singularity behaviour. Our theoretical analysis consistently predicts and subsequent single-cell level observation directly proves that desynchronization of individual cellular clocks underlies singularity behaviour. Our theoretical framework also explains why singularity behaviours have been experimentally observed in various organisms, and it suggests that desynchronization is a plausible mechanism for the observable singularity of circadian clocks. Importantly, these in vitro and in silico findings are further supported by in vivo observations that desynchronization underlies the multicell-level amplitude decrease in the rat suprachiasmatic nucleus induced by critical light pulses.