Is there a common saying in English that means "It's just business, I don't feel any shame"

"Nothing personal, it's just business."

Coined by Otto "Abbadabba" Berman an accountant for the Mafia in early 1900’s in New York. See Wikipedia

In The Godfather movie, Michael Corleone likewise says: It's not personal. It's strictly business.
See YouTube

business is business

In The Free Dictionary:

A phrase that emphasizes business decisions as completely separate from emotions or personal issues.

In Merriam-Webster:

used to say that in order for a business to be successful it is necessary to do things that may hurt or upset people

Exactly how "immoral" an action can be and still be covered by these sayings is perhaps a question for a different venue.