He wakes up a quarter of an hour before sunrise and delays purifying himself because of waswaas; can he do tayammum?

Praise be to Allah.

Firstly: 

We ask Allah to heal this brother and grant him well being, because waswasah is a disease and a problem. 

Secondly: 

If a person wakes up and there is only a quarter of an hour left until sunrise, this is sufficient time for him to do wudoo’– and even ghusl – and pray, so it is not permissible for him to do tayammum. 

Similarly, if he wakes up in a state of janaabah and the time is even less than that, he should do ghusl even if the time for the prayer ends. See the answer to question no. 94311. 

This person who is affected by waswasah should fear Allah and realise that delaying the prayer until the time for it is over is one of the gravest of major sins; the same is true of praying without being in a state of purification when one is able to do it. So let him hasten to purify himself and pray, and let him convince himself that this is the shar‘i ruling that is binding in his case. Perhaps this will distract him from the waswasah. 

And Allah knows best.