//this method in the userControl
public void Clear()
{
   //Clear your text box
   this.txtbox1.Text = string.Empty;
   //Do other clean-up things if you want
}

private void button1_Click(object sender, EventArgs e)
{
   //Call the Clear method from the UserControl
   yourUserControlName.Clear();
}

private void button1_Click(object sender, EventArgs e)
    {
        YourForm();
    }

public partial class UserContoleName: UserControl{
  private static UserControleName _userControleName;
  public static UserControleName Instance{
   get{
     if(_userControleName == null){
       _userControleName = new UserControleName();
      }
return _userControleName;
}
}
public void Clear(){
this.txtbox1.Text = string.Empty;
}

private void Button_click(object sender,EventArgs e)
{
  UserControleName.Instance.Clear();
}