Hello Kitty doesn't have a mouth because she communicates through her heart rather than in words; she is supposed to be a universal character not tied to any particular language. She also is not supposed to be linked to a specific emotion, so that people can project their current feelings onto her.
Hello Kitty is currently designed by Yuko Yamaguchi, who wants her to appear happy when viewers are happy and sad when viewers are sad. Recently, Sanrio revealed that Hello Kitty is not a cat, contradicting popular belief. Although mouthless, she is supposed to be a little girl in cartoon form. Hello Kitty actually has a pet cat of her own.