//I assume the attachment contains some sort of malware but what is the objective of the spammer?//
The attachment might contain malware, but could equally contain a form to fill in or a link to a website as a phishing attempt - i.e. an attempt to get you to reveal sensitive info.
// Would the malware help them access my hard drive or emails?//
If there is malware, it might do any number of things - install a key-logger, or the crypto virus, or a variant, in order to blackmail you, or simply install a bot so that your machine can be used as part of a network for other nefarious purposes.
//Is it just to cause mischief /disruption?//
Rarely: most modern malware is about making money.