I'll have it done by tomorrow.我将在明天前【让人】完成这件事.

have sth.done  等于省略了无需指明的 by sb..即“让某事被某人做”.

如果要指明“让某人亲自做”就不能用过去分词,应该改用由不定式表示的主动形式have sb.do sth.如：

I'll have him do it by tomorrow.我将让他在明天以前完成这件事.
I will have the doctor pull my bad tooth tomorrow.我明天要让大夫把我的坏牙拔了.

如果是要自己亲自做,把 ab.改为反身代词即可——

I'll have myself do it by tomorrow.我在明天以前要亲自完成这件事.
I will have myself pull my bad tooth tomorrow.我明天要亲自把我的坏牙拔了.