My mum was recently diagnosed with cancer. Should I tell my supervisor?
Many countries have rules in place that allow employees to take paid or unpaid leave to care for an ill relative. No shame or unprofessionalism should result from making a request to accommodate a need to deal with a loved one's illness.

If you have a good relationship with your advisor, then your advisor should understand. 

(That said, the advisor may or may not have much control over the viva, depending on who is responsible for scheduling and organizing it, and who else must attend. But you won't lose anything by asking.)