Disavow the domain
What can I do if I want do disavow a subdomain? i.e.
spam.site.com. I'm also assuming that if I were to disavow the domain it would include all subdomains?
In addition to Geoff's answer:
When you talk about disavow, are you talking about Google's Webmaster Tools disavow links tool? If so, then this isn't the correct way to go about it; I will explain at the end.
Firstly all domains, for example:
So in a simple way
Now expanding this,
Now thinking about this I'm sure you can now understand that
Now with regards to disavowing links, if you mean Google Webmaster Tools disavow links, this option should only be used after all necessary manual removal of the links has been made as this will show Google that you have taken the time and effort to amend whatever it is that you are doing (this is more in the case where you have been penalized by Google for unnatural links, etc...).
So in summary:
No, it doesn't work like that.
A subdomain is treated as it's own entity so you'd have to disavow subdomains separately like so:-