Yes. Much of it was adopted as American law. Much of it was rejected. The aspect of English law regarding "subjects" was specifically and explicitly rejected.
“The common law of England is not the common law of these States.” –George Mason "
Rather they objected that the King did not abide by it in regard to the colonies. "For abolishing the free system of English laws in a neighboring province, establishing therein an arbitrary government, and enlarging its boundaries so as to render it at once an example and fit instrument for introducing the same absolute rule in these colonies..."[emphasis added]
That was while they were colonies of England. Once the decision had been made to become independent, they eradicated parts of it root and branch. Our Entire Bill of rights was specifically created to reject certain aspects of British law.
Here is what Constitution.org has to say about Common Law as a source of the Constitution:
Blackstone's Commentaries (1765) Considered the book that "lost the colonies" for England. This text delineates the legal principles of common law which ensure the fundamental rights of Englishmen. Blackstone was quoted by the colonists twice as often as they quoted Locke. [emphasis added]
That the colonists were not being given the consideration that ordinary Englishmen had is not in dispute. Protesting their lack of rights as Englishmen was part of what initiated the move to independence, but after having declared Independence and tasked with the creation of a new government, the Now Federalists improved upon English law by creating many new rights and safeguards not part of English law. They created New American law.
I suggest you read the context for this quote. Mr. Mason is not proclaiming the advantages of this difference, he is concerned that some protections of English common law will be lost. He speaks of the Common Law of England which " prevented a dismemberment of their country" and "has prevented the power of the crown from destroying the immunities of the people." The quote you posted is immediately followed by: "I conceive, therefore, that there is nothing in that [US] Constitution to hinder a dismemberment of the empire."