If you have the new mirror cover then you should be able to look at it and determine what is holding the old mirror on.
I never replaced a 2nd gen mirror so I don't know exactly how they are attached - the 1st gen mirrors are tough to remove without breaking 1 or 2 of the retainers. The bottom retainers are difficult to get to - you have to remove the mirror to get to them.
Removing plastic cover from a 2015 Hyundai Elantra Side View Mirror - YouTube
I never replaced a 2nd gen mirror so I don't know exactly how they are attached - the 1st gen mirrors are tough to remove without breaking 1 or 2 of the retainers. The bottom retainers are difficult to get to - you have to remove the mirror to get to them.
Removing plastic cover from a 2015 Hyundai Elantra Side View Mirror - YouTube