"You don't clear a SIM card"
Actually, many phones allow you to save contacts to the SIM for an easy way of migrating them to a new phone, and you can delete them from there too. Only downside to saving them there is you can only have name & number, no other info.
On your phone, you need to switch to SIM card for contacts on the display, then use options to edit or delete.
Or buy a SIM reader and delete them with that.