On Saying Goodbye To A Special Acquaintance.

[Brownlie]

On Saying Goodbye To A Special Acquaintance.- Two prepositions in the title, consider making it more condensed.
 
Released toward infinite limbo, my mimic’s hand -- The enjambment without punctuation is confusing.
Parts and cries with the palm it craves and
Plagiarises with every breath. She takes -- Kind of interesting idea. Your splitting the self here, and you know, going towards madness, which is always fun. 
And makes a newfound exit, few mistakes -- Can't tell what a newfound exit is. 
Shake her path, unlike mine, confined;
My accursed time unwinds with wine, -- With all the i's in this line, the line stands out. However, I don't think this is your strongest line. 
For now we’re lost, stuck in the vestibule -- A vestibule is a nice liminal place for a parting, between coming and going. However, "for now" is kind of sloppy English when the poem should probably use more precise wording. 
That we are never to reach beyond
Our first door’s welcome. Abscond
To cowardly safety; ‘tis not for I- -- You've got a sort of Prufrock thing going on, but I don't like "tis" unless your aping earlier versions of English. 
I die, in a different manner, my eye
Bloodshot; yours bland as butter, -- Hey, I really like bland as butter.
Hear the sandy wind, the mild mutter
Of an unfulfilled, complacent life
Upon your conscience; heavy, rife.
Your doing, your will; your brow
This is upon. I’ll leave you. How?
I do not know. Ciao.

I liked the bland as butter description, and there's a good vocabulary in here. However, I don't think you've articulated what you want to be saying here to the best of your ability. If you want an exercise for revision, you may want to write what you're trying to express in clear prose and then edit that into a poem. Good luck.