1. to launch; to shoot up; to hit (a ball) high
彼は似たようなボールを今度は真上に打ち上げていた。This time, he was hitting a similar ball straight up.
2. (of waves) to dash; to wash up (ashore)
発見された時、僕は、この近くの浜に打ち上げられていたって。They say that when I was found, I had washed up on a beach near here.
3. to finish (e.g. a theater run, sumo tournament); to close
芝居は明日で打ち上げる予定だ。The play is scheduled to close tomorrow.
4. to report (e.g. to one's boss)