I really have no practical experience of teaching ESL to deaf non-native speakers.

You are using "deaf mute". Does that mean that that child cannot speak either? I know a couple of deaf people, and I also have some long-term experience of communicating with them. These deaf people have learned to read from my lips and to use deaf-sign language. They can also more or less speak/articulate themselves clearly. With this profile in mind, I can state that one such deaf person I have seen learning Norwegian, both written and spoken and mastering German both written and spoken quite proficiently. The same deaf person is learning English now, spoken and written at the age of 52! This person is an Italian native speaker and one of the co-priests in the Anglican parish I am serving on weekends (I have another full-time volunteer job in an educational ministry).

I am quite convinced that deaf people are able to learn foreign languages including ESL. But it seems that they need to be able to articulate themselves in their native language first; otherwise, they might also not be able to express themselves in a foreign language.

The only practical advice I can give is that you teach this child as a co-teacher with someone who has been trained especially for teaching the deaf.

Good luck!