We learn from Yahya ibn Musa who learnt from Sa'eed ibn Sulayman who from Muhammad ibn Khalid Qarshi who from Dawud ibn Husayn who from lkrimah and he from Ibn Abbas (RA) that the latter was asked about tayammum. He said, "Allah, the Exalted has given the command for ablution in His Book saying: “Wash your faces and your hands up to the elbows”
(5: 6)
Wipe your faces and hands with it.
And Allah said: “And the thief, man or woman, cut off the hands of both”
(5:38)
It is known from Sunnah that the hand is amputated up to the ankle joint. Hence, tayammum too is of the face and hands (up to joints).