you need to run a whole new wire from the clock to that box. lol I had to,couldnt resist. Just splice it back together man, it will be fine. strip about an inch of wire off,twist them together.you dont want to WRAP one around the other one,thats not a good connection,they should be intertwined. put the two wires next to each other,make a v,and twist from the bottom of the v. your probably saying i know how to twist a wire lol. but a strong connection is a good thing. make sure you twist the wires together,in the way the wire nut tightens,or the wire nut your gonna put on will twist them apart,and you will have an intermitent connection.
I agree
^ But I need to add one thing.
Use gel caps/inserts to keep water out. Water will ruin the connection overtime and make it rusty if you just put a wirenut on there