There were two ways of doing it.
In case of Tirek, losing a cutie mark was a visible cue that a pony's magic has been drained - in that case the pony would lose all natural magic - not only spellcasting, but any SU or even EX abilities she might possess (that includes any abnormal strength for earth ponies, as well as pegasi flight - their wings are too small to lift them naturally)
In case of Starlight Glimmer's "=" spell, the cutie mark was stolen and kept in a jar (it would fly back to its owner when released) and the "=" mark lowered all the pony's stats to average for her race, as well as actively hampering any attempts to do whatever the pony used to excel at.