Faster way break apart lines?

I have a master map with lots of topo lines, roads, etc. I need to "cut out" individual maps from this master map. Currently I add a point where I want to "cut" on each individual path and "break apart" each line. This process is very time consuming and inefficient, there must be a better way. Help please?

(I'm coming from Freehand where I could just select all of the individual lines together and use the knife tool to cut along the lines I needed to then extract just the map I wanted)