How to programmatically remove a field from a node?
field_delete_field($field_name) will mark the $field_name for deletion on next cron run.

You could use field_purge_batch to do the deletion, if you don't want to do it on cron run.

EDIT: field_delete_field() should be used when you need to delete the field from other bundles as well. If you only wish to delete the field from a particular bundle you should use field_delete_instance() as mentioned by @Clive.