In short, no.
The Saxon Math Homeschool textbooks were published prior to the advent of Common Core in 2010.
And most of the Saxon Math "School Line" of books was also published before 2010.
There are a few versions of the school line of Saxon Math books that were republished to include a list correlating the lessons to the Common Core standards but the teaching was not changed at all.
It is important to note that Common Core is not a math curriculum nor is it even a math style/approach. "Common Core" refers to the standards that were adopted by most states. The purpose of these standards was for all third graders to be learning the same concepts no matter which state they lived in. The purpose was not to teach math a specific way.
Saxon Math basically has the same standards for each book level that the Common Core standards list for each grade.