Is 你看看自己 correct for daily common speaking in Mandarin language?
Both are correct, and both have similar meaning. These two phrases could be used to blame on someone for something.
E.g.
你看看自己這副無精打采還病懨懨的樣子, 誰看了都討厭。
你看看你, 跟你說不要亂碰你還碰, 結果現在果然受傷了吧。