It has been proposed that cancer cells, in particular glioma tumour cells, secrete a chemorepellent factor that guides cell migration away from the tumour, facilitating migration and invasion. We present a hybrid continuous-discrete mathematical model of tumour growth and the chemotropism phenomenon to show that such a chemorepellent factor can also act as a promoter of self-metastases, a mechanism for tumour expansion we have previously shown can explain several essential kinetic dependencies of tumour growth. A sufficient criterion for this expansion was found to be the passive migration of peripheral cancer stem and non-stem cells away from the main tumour mass, where migrating cancer stem cells form new clusters. We show here how the introduction of an active repellent trait serves to accelerate peripheral migration and thus, by the self-metastases principle, accelerate tumour growth. These results provide a mechanistic basis for the proposal that chemorepellent action in gliomas may underlie their rapid growth.