Reference: Fataawa wa Rasaa.il Shaykh ‘Abdur-Razzaaq ‘Afeefee – Page 386, Fatwa No.10
Question: Is it correct to do tayammum with the dust/sand which is on the prayer mat?
Response: If he is unable to find water for wudhoo, then he can strike the prayer mat [with his hands] and if any dust/sand comes out then he can do the tayammum with it. If no dust/sand comes out, then it is not correct [to do the tayammum]. Likewise, it is not correct to do the tayammum [by striking the] wall [with the hands] unless there is any dust/sand on it. However, if a person is in need of [doing] tayammum, then he can gather some dust/sand in a [clean and dry] container and [then] perform the tayammum with it.