broken coax cable

i have this coax cable i want to use but soneone (probably me) step on one end O_O   
the core is undamaged i think    but its still a bit hard to get the cable into the t-connector-thingy
i it safe to use?   

Sure it's safe. Replacing the end connector would cause more problems than it solves, so don't bother if the cable still works.