"From America" - Back then, the whole western hemisphere or "New World" was called America (still is by non-Yankees). The "shipping" was from Venezuela and points South and West. By the time the colder "North" was settled, African Slavery was well established in the warmer areas.
"handle the stress of labor" - more like handle the Smallpox. The entire native populations of many Caribbean islands were 100% eradicated by disease, forced labor, torture, and warfare.
"[master] started to fuck his slaves" - outside the thirteen colonies not so much. The Spanish and Portugese were not hampered with the f&*ked moral values that permeated the thirteen colonies. They had sex with their own women. Also, in the thirteen colonies, there was a major change in the law that facilitated race mixing:
Traditionally, a child inherited the status of his father. So a child born of a master and a slave woman was free. In the thirteen colonies, the law was changed so that a child inherited the status of his mother - a child born to a slave woman was a slave.
Another thing unique to the thirteen colonies was the deliberate effort to erase all traces of African Identity. Speaking in African languages was prohibited; african garb, religion, and drums were outlawed; families were broken up and sold. These things did not happen in other parts of America.
In the Caribbean, with a tiny native population and a large slave population, the slaves remained Black. They also retained their ethnic appearance, culture, language, and values.
In Central America, with a large native population compared to the slave population, the mixing of African and Native-American slaves resulted in the assimilation of the Africans. Particularly in Mexico north of Vera Cruz, less so south into Columbia (now Panama).
In South America, with large populations of both Africans and Natives, race mixing resulted in a broad spectrum of colors and features.
So, the situation is a little more complex than "nothing but a mixed race".