edit: this is how I have always applied the rule myself: when on airways or on a direct clearance you are responsible for your own terrain clearance, when being radar vectored ATC is responsible. ATC has minimum vectoring altitude charts which will be below MSA published altitudes.
PANS-ATM 8.6.5.2 says:
When vectoring an IFR flight
and when giving an IFR flight a direct routing which takes an aircraft off an ATS route, the controller shall issue clearances such that the prescribed obstacle clearance will exist at all times until the aircraft reaches the point where the pilot will resume own navigation. (My
bold.)
The usual caveats about division of responsibility apply.
"Disregard the SID , after departure route direct to XXX" is, in the absence of omnidirectional departure procedures, somewhat lax. I would expect at the very least, "after passing altitude yyyy ft, route direct to XXX".