ORS 807.550 says "A person commits the offense of holding multiple licenses if the person applies for and accepts a license or driver permit, other than an instruction driver permit, when the person holds an existing license or driver permit". There is a corresponding regulation Driver and Motor Vehicle Services Division 735-062-0096 elaborates, procedurally
(1) When DMV issues an interim driver card or an interim
identification card to an applicant under OAR 735-062-0094, DMV will
invalidate and return the driver license, driver permit or
identification card the applicant surrendered. An invalidated driver
license or driver permit may not be used as proof of driving
privileges, but is not deemed cancelled under ORS 801.175.
(2) DMV will invalidate a surrendered driver license, driver permit or
identification card by hole-punching the card.
(3) The invalidated driver license, driver permit or identification
card must be destroyed by the applicant when:
(a) A valid driver license, driver permit or identification card
issued and mailed by DMV is received by the applicant; or
(b) Driving privileges or rights to an identification card have been
suspended, cancelled or revoked.
This suggests that it is possible that your mutilated, invalidated permit is returned but you are not in possession of a replacement, for example the new license is not mailed to you at the same time as the cancelled one is mailed back. At any rate, it is not legal to keep the old cancelled one, and still have its replacement.