Live frugally? Say personally that's untrue (4,7)

'live frugally?' is the definition.
I know nothing about this answer so I can't tell whether it can be defined by this definition.

'personally that's untrue' is the wordplay.
I cannot really see how this works, but
'personally' could be 'oneself' (I've seen this before) and 'oneself' is found within the answer.
The remaining letters 'deny' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'say' is the link.

Can you help me to learn more?