Tim Gibson teaches us how to tape and finish textured drywall in this tutorial. To begin, use a scraper to scrape off any texture around the join. This will leave 4-5 inches to replace the joint. If it doesn't come off easy, use a sponge to wet the area on both sides before you scrape it. After this, use either fiberglass tape or paper tape with drywall joint compound. If you use the compound and paper tape, you have to put a thin layer of compound down before you place the tape over it. Let this dry for 24 hours, then do one more layer and let dry again. Once this is done, put the last coat on thick and use a knife to get the same finish like the original drywall looks.
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