Can i separate a tweeter from a woofer?

so in my prelude theres a spot on the door for a woofer and a spot on the dash for tweeters with a crossover hidden somewhere in between. when i run 2 way speakers in the doors the tweeters sound really horrible because there only getting low frequencies but the woofers sound fine... i was wondering if i could remove the tweeters from the two way speakers and use them to replace the factory tweeters in the dash which are blown.