don't disturb me能这么说吗?谢谢

我觉得可以。

可以的，disturb是及物动词

disturb
vt.
打扰, 妨碍
Don't disturb him.
别打扰他。
使焦虑, 使烦恼
His passion for his cause disturbed me.
他对事业的热情使我焦虑不安。
扰乱, 弄乱
I felt disturbed to hear of your illness.
听说你生了病, 我感到不安。

Leave me alone，please！

如果是别烦我的意思，我建议用leave me alone
你这么说也没错...

同一楼上的。你的说法虽然没错，但是不够地道。

leave me alone 比较好