cut someone's throat
1. Be the means of someone's ruin, as in Joe would cut her throat if she got in his way. One can also cut one's own throat, that is, spoil one's own chances, as in Alice cut her own throat by her repeated absences. This hyperbolic term alludes to actual murder (or suicide). [c. 1500]
2. cut one another's throats. Engage in destructive competition. For example, With their price war the two stores were cutting each other's throats. This usage gave rise, by 1880, to the idiom cutthroat competition, for vicious competitive practices.