Can Behavioral Health deny me getting a second opinion off post?

Not Normally, but it will come out of your pocket.

They can't. But as stated, you'll have to pay out of pocket.
Or you could always to your friendly unit PA, explain whatever the situation is, and that you would like a civilian second opinion, he/she/it can order the referral.
I did it while still in.

Behavioral health the department, no. But if you are asking about Tricare coverage then you need call Tricare and explain what’s going on. They may be able to approve a special type of authorization.