Hi,
you cant have two submit button on one form, do one thing:
have two simple button< input type="button" value="delete"......> and have on hidden field in form with name "task".On onclick event of these button call a function where you set the value of task="delete" or whatever you want, after this submit the form using javascript.
On server side check the value of task, according to value you take the action( either delete or add or....), one more thing in all cases you'll be having only one php page, where you will perform action according to "task" value.
Have a nice time !!!