According to sanrio.com (the company who makes Hello Kitty products):
Why doesn't Hello Kitty have a mouth?
Hello Kitty speaks from her heart. She’s Sanrio's ambassador to the world and isn't bound to any particular language.
But according to the host of the late-night QVC show I watched recently, there's an additional reason as well! The host said that Hello Kitty is more relatable to people when she isn't showing a set emotion. Without a mouth, she can appear to be feeling however the person playing with her is feeling.
I can see that. Imagine an emotion and look at Hello Kitty - she could be feeling that way, too.