Stopwatch mywatch = new Stopwatch();

کد فوق نباید درون متد button3_Click باشه، باید بعنوان یک فیلد از کلاس معرفی اش کنید:

Stopwatch mywatch = new Stopwatch();

private void button3_Click(object sender, EventArgs e)
{
SoundPlayer sp = new SoundPlayer(@"F:\Programming\GhazalNama\GhazalNama \GhazalNama\Resources\WAV\4.wav");
if (button3.Text == "Start")
{
mywatch.Start();
button3.Text = "Stop";
sp.Play();
}
else if (button3.Text == "Stop")
{
mywatch.Stop();
sp.Stop();
button3.Text = "Start";
double TimeSpent = mywatch.ElapsedMilliseconds / 100D;
label2.Text = string.Format("Elapsed time :{0} Seconds", TimeSpent.ToString("#,##.##"));
}
}