My mom take thyroxine sodium tablets 100mcg everyday,and her tsh laval is >60, so this this thiroid is primary or not?

This is primary: hypothyroidism, and it is not sufficiently treated.She needs a higher dose of replacement and then have her levels rechecked as often as necessary until her levels have returned to normal.

Needs more: Sounds like she's undertreated. Might need a higher dose of medication to achieve adequate control of her thyroid and lower the TSH.