You can redirect standard input and use a StreamWriter to write to it:
Process p = new Process();
ProcessStartInfo info = new ProcessStartInfo();
info.FileName = "cmd.exe";
info.RedirectStandardInput = true;
info.UseShellExecute = false;
p.StartInfo = info;
p.Start();
using (StreamWriter sw = p.StandardInput)
{
if (sw.BaseStream.CanWrite)
{
sw.WriteLine("mysql -u root -p");
sw.WriteLine("mypassword");
sw.WriteLine("use mydb;");
}
}