Special orders are just orders relating to specific people (as opposed to general orders). I'll quote one from the regiment I've studied below.
Because they're about specific people, you won't find them published.
But you can order a copy from the National Archives, if you know who issued the order. (Was it his regiment? the brigage? division? corps? ....) Or they might be able to find it in the regimental orders book--at least the one for my regiment includes copies of orders relating to the regiment. (I haven't ordered copies from them for a while, but I'd expect it to cost whatever their minimum charge is.)
Harry
===========
Head Quarters 5th Army Corps
July 3rd 1864
Special Order No 160
Extract
The following enlisted men are hereby honorably discharged the [sic] service of the United States, to enable them to accept commissions in the Volunteer Service
Sergt Theodore H Hope Co "E" 91st Penna Vols. to date July [1st 1864]
x x x x
By Command of
Major Genl Warren
Signed Fred. T. Locke
Asst Adjt Genl
Head Quarters 1st Division 5th Corps
July 3rd 1864
"Official"
(Signed) C. B. Mervine
Asst. Adjt. Genl
Head Quarters 2nd Brigade 1st Div. 5th Corps
"Official" July 3rd 1864
(Signed) E. C. Bennett
A.A.A.G.
Head Quarters 91st Reg. Pa Vols 2nd Brig.
1st Division 5th Corps July 3rd 1864
Official
B. J. Tayman
Adjutant