죽이다 is the causative of 죽다 — to kill — and the -아/어 verb in front says by what means: 밟아 죽이다 trample to death, 찔러 죽이다 stab to death, 쏴 죽이다 shoot dead, 굶겨 죽이다 starve to death. Much of this is folk-tale and drama language. Note that 잡아 죽인다 and 쳐죽일 놈 work as curses rather than statements of intent, roughly English 'I'll kill you' and 'that damned so-and-so'.