I have tried browsing examples, but the only potential difference I see is that you can say "它也会杀死庄稼", but I am not sure if 杀害 also refers to plants.
害 in 杀害 (kill; murder) means 'victimize'. You can only victimize creatures that have emotion, capable of feeling pain. '杀害' mostly refer to murder of human; And only killing of human can be deemed 'murder'
Note: only human intentionally killing other human is called 'murder' . A tiger killing a human is not a murder, but a killing
杀死 (kill someone/ something dead) can apply to any living organism, from single cell bacteria to human
For most case, the 杀害 emphasizes on the purpose(the intention of killing), and the 杀死 emphasizes on the result:
In 杀害, the
害are both verb, and both meaning to kill, they almost have same meaning, just the
害is more like make it suffer, so 杀害 shouldn't refers to plants, unless it's personified to suffer.
And in 杀死, it means kill something dead, the
杀is the kill part and
死is the dead part, so it can refers to anything that is alive and can die, like plants in your case.
Just share some of my own understandings here.
杀死 and 杀害 are all verbs. 杀死了 and 杀害了 show results.
杀死 is just a statement of fact, but 杀害 is accompanied by human's emotions.(Most are pity and compassion emotions)
For example, a good leader is murdered by terrorists or a loyal minister is assassinated by traitor. If you use 杀害, more expressive of your regret for the dead. If you use 杀死,just statements a fact without human emotions.
杀害 implies killer has bad intention while 杀死