This is a jukugo word that uses the on'yomi readings of the kanji. You haven't learned this reading for 手 yet, so here's a mnemonic to help you:
To be a good pitcher, all you have to do is put the ball into the chute (しゅ). Pitchers don't actually throw the ball. There is an invisible pitching chute right on the mound. You slide the ball into the chute and off it goes!
How much is the doll of the pitcher, Darvish?
The pitcher, Tanaka, lives in 2-Chome.
Who do you think today's starting pitcher will be?