Mischievous is the standard spelling of the adjective meaning causing mischief. Mischievious is a misspelling, but it is so common that it may someday gain acceptance. For now, it doesn’t regularly appear in edited writing, and dictionaries and spell check have yet to accept it, for what that’s worth.
The misspelling is not new. The OED lists instances of mischievious going back to the 17th century, and a Google Books search reveals a few thousand instances from before 1920. So while mischievous is certainly the standard spelling and is safer in formal writing and school papers, using mischievious is not a grievous error in informal contexts.
The misspelled form is rare in 21st-century published writing because spell check catches it, but it does appear from time to time, even in edited publications—for example:
We were good friends, and I will always remember him for the warm, sincere and yet mischievious grin. [Morning Sentinel]
She remembered his mischievious side. [The Star Ledger]
But mischievous is far more common in editorially scrupulous publications—for example:
It is Dionysus, the mischievous god of revelry. [Financial Times]
My guess is Ms. Shemy will find some mischievous ways to make it work. [New York Times]
Tongue-in-bearded-cheek, Ben Hudson has a typically mischievous take on where his retirement will leave the Western Bulldogs. [Sydney Morning Herald]