Never like the mirror's either placed our family pictures in fact the family grow so big the frames were increased to accommodate them all.
My mirror was as Gary described Velcro strip on bottom and metal clips at top after you lift mirror off them.
Use a steady pull on bottom and it will release than just lift.
If you have a large frame for all you pictures and maybe added little ones will hide any screw holes or you can use a wood filler.
My wife likes pictures and they are in bathroom's, bedroom and living area.
Makes it more homey that way.