I'm finding it difficult to play super Mario with the analog joystick. Is there any way that I can turn it off and just use the d-pad on the left of the controller instead?
No. Like most Nintendo 64 games, there's no option to use the D-pad. It had no function in Super Mario 64. If you're not playing on an actual Nintendo 64, however, you may have other options.
As an aside, Super Mario 64 DS for the Nintendo DS is a remake of the original game which can use the D-pad for movement. Note that it's not the exact same game, but they are very similar experiences.