Speakers and crossover wiring

Hi all - I am replacing the stock speakers in my 2007 Avalanche. I have read a lot of the posts about wiring (which has been really helpful!), but I am left with a pretty basic question.  I am a little confused on how to wire the crossover.  The front door speaker and the tweeter both have existing wiring to the factory speakers.  Am I supposed to cut the plug off the factory wiring and route that to the crossover?  And then run new wiring from the output side of the crossover to the speaker and tweeter?

Thanks!