There is no option to delete or remove system attribute in magento admin.
I would suggest not to delete any system attribute. But as per client's requirement if you want to remove some attribute then you need to do following settings:
1) Go to PhpMyAdmin.
2) Go to your database.
3) Go to eav_attribute table.
4) Search your attribute_code.
5) Edit that attribute_code's row.
6) Set 1 in 'is_user_defined' column.
7) After setting 1, you can go to magento admin. Here, you will find that the attribute which is set 1 for 'is_user_defined' is no longer remain system attribute.so you are now able to delete it.
I will suggest you that do not delete any attribute if you don't want. Better to remove it only from desired attribute set if you don't require it.