Dr Yang told the BBC: "We recognise we are still at the early stages of research and development.
"We know we have an audacious vision of a world with no shortage of organs, that is very challenging, but that is also our motivation to remove mountains."
Pigs are particularly promising for xenotransplantation as their organs are a similar size to humans', and the animals can be bred in large numbers.
But removing the viruses is only half the challenge, even organs donated from other people can cause a strong immune reaction that leads to the transplant being rejected.
The US team is investigating further genetic modifications to make pig organs more acceptable to the human immune system.
Darren Griffin, a genetics professor at the University of Kent, said: "This represents a significant step forward towards the possibility of making xenotransplantation a reality.
"However, there are so many variables, including ethical issues, to resolve before xenotransplantation can take place."
Prof Ian McConnell, from the University of Cambridge, said: "This work provides a promising first step in the development of genetic strategies for creating strains of pigs where the risk of transmission of retroviruses has been eliminated.
"It remains to be seen whether these results can be translated into a fully safe strategy in organ transplantation."
The researchers had to overcome unexpected challenges from performing so much gene-editing in one go.
The Crispr technology works like a combination of a sat-nav and a pair of scissors. The sat-nav finds the right spot in the genetic code, and then the scissors perform the cut.
But making 25 cuts throughout the pig's genome led to DNA instability and the loss of genetic information.