Not the same were used during the Antebellum period of the United States. For example crucifixion would likely not be used, and I have not heard of it ever being used, mainly because of the relationship of crucifixion with Jesus Christ and Christianity.

Most slave memoirs from the period, such as "Diary of a Slave Girl" and Fredrick Douglas's papers mostly noted that whipping was the preferred method of discipline in the South during the period. Often they would say that the wounds would seep down to bone if the master was cruelly harsh. In the memoir by Mary Prince, she talks about how she once saw a man tied to a pole being whipped bloody and then stabbed in the foot with a bayonet. She also talked about the torture of everyday life, such as working on sugar plantations and also the daily sexual torment of being a slave.

These methods of "discipline" were different than ones used during the classical because it was a different time.

The severity and frequency of slave discipline varied in time and place in colonial and antebellum US (which century, urban vs. rural, gang vs. task system, agriculture vs. skilled trade, a society with slaves vs. a slave society, etc).

The level of violence grew as slavery grew in Virginia during the colonial period. In the 17th century, whipping, maimings, brandings and beatings were common, but, in the 18th century with the rise of the plantation economy, new forms of discipline emerged designed to humiliate and demoralize including the drinking of urine and making runaways wear metal bits in their mouths like horses. Other extreme cases included placing slaves in coffins and crushing them. Typically, a slaveholder and his agent would not be held legally responsible for the death of a slave if the death occurred during "correction." (Ira Berlin, Many Thousands Gone).

I suspect slaves were not crucified because of the religious symbolism of crucifixion with the framework of western Christianity. I haven't come across a reference of a crucified slave in the Americas.

One reference comparing Roman to New World slave discipline occurred in Brazil. "Numerous travelers and commentators stressed the lack of restraint or interference with the save punishment of Brazilian slaves, who (reminding us of the treatment of slaves in ancient Rome) 'were burned or scorched with hot wax, branded on face or chest, tortured with hot irons, had their ears or noses lopped off, or suffered sexually related barbarities as the result of jealousy.'" From David Brion Davis, Inhuman Bondage, (New York: Oxford University Press, 2006), 118.