Given sufficient non-damaged genetic material, it should be possible to create a genetic clone of Wolverine.
This was tested and partially successful in the creation of X-23.
Seeking to take the project in a new direction, the project's director, Doctor Martin Sutter, recruited renowned mutant geneticist Doctor Sarah Kinney and tasked her with creating a clone. Using the only available genetic sample from Weapon X, which was damaged, they were unable to salvage the Y chromosome after 22 attempts. Kinney then proposed they create a female clone, and though her request was initially denied, she still went ahead and produced a viable female subject, prompting Sutter to reconsider. Despite resistance from his protégé Doctor Zander Rice, whom he had raised after Rice's father was killed by a bestial Wolverine at the original Weapon X Project, Sutter allowed Kinney to proceed. As revenge for her insubordination, Rice forced Kinney to act as the surrogate mother for the clone, and she gave birth to "X-23."
X-23 was a genetic clone with the same powers and general temperament, but was not an exact opposite-sex duplicate. As she was only a genetic clone, she had none of the training or memories of Wolverine.