救起

起 (qǐ) here is a directional complement meaning 'up' — the rescuer is pulling someone up out of danger (water, a hole, debris). Use 救起 specifically when there's an upward motion; for general 'rescue,' use 救 (jiù), 救出 (jiùchū, 'rescue out of'), or 营救 (yíngjiù, more formal).

mistakes

救起 takes only animate objects — you save people and animals, not abandoned plans. For 'rescue a project,' say 挽救 (wǎnjiù) or 拯救 (zhěngjiù).