Most form spam is submitted through a script designed to automatically send the spam and there are ways to combat it.
In your case, the reason you're still getting spam from the form you deleted is because once the script gathers the necessary information it can continue to send the details even if you delete the form. To stop it, you also need to delete or move the file(s) that process your form on your server. (If you look at a the HTML for your form, there will be code containing
form method= - either
get or
post - followed by
form action - a URL to your script.)
**Don't remove the form processing file if other forms on your site are using it. Rename it or move it and make sure you update all your website forms.
Renaming the file is a temporary fix. The spammers will find the new information and start spamming you again.
One more permanent solution is adding a CAPTCHA to each form. (A CAPTCHA is a randomly generated text strings that the user has to correctly enter in order to submit the form - spam scripts can't handle them). There are several scripts available that you can probably find via a Google search. It's been a long time since I've used one, but when I did, I used
http://www.protectwebform.com/
CAPTCHA's can dissuade some users from completing forms so don't use them on any that are highly important (for example a lead capture form).
Another permanent solution is a form script with built in security features, including the ability to thwart the spam scripts. Again, there are many available. I like Master From V4
http://www.willmaster.com/software/formV4/
(
not an affiliate link)
These solutions won't stop human spammers from filling out your forms, but they'll stop the vast majority of the spam because most comes from automatic scripts.