Korean or chinese romance drama with a mute girl? 

Wuri's Family it aired in 2001 if you don't mind watching older dramas

  • One and Only - Chinese historical romance drama. The FL is mute for part of the drama
  • Love in the Moonlight - Korean historical romance drama. A young girl in the palace is mute. She isn't a main character, but she contributes to the plot and has several scenes that revolve around her being mute / finding alternative ways to communicate with the leads. 

Also:

  • Silence (Taiwan drama)