At times joomla is targeted for major spam usage by hackers bots.
There is not much that can be done but try and enabling captcha under plugins and then global configuration for joomla.
If that does not work they may be attacking the contact user itself.
Check your access logs to see if this is the case.
If the URL being hit alot is
option=com_content&view=contact&id=
Try disabling the contact extension as it not required much be websites by going to:
Extensions -> Manage - Manage and disable the contacts extension.
