I don't think you have to worry about malware running from within the clipboard, unless you're manually pasting commands in an attached file into your terminal.
I guess they could try to read/write to the clipboard via some browser, see here https://stackoverflow.com/questions/5551338/how-to-read-clipboard-data-in-cross-browser
On a more serious note, a general rule of thumb when dealing with malware is to do so in an isolated environment, such as within a virtual machine with limited access to its host, and if it has an internet connection, maybe add firewall rules so that it can only ever connect to a white-listed analysis website.
One of my favorite "hacking" scenes in any movie was in the bond movie, Skyfall. In the film, the young and (apparently) foolish Q decides that it is perfectly safe to plug in the villain Raoul Silva's laptop into MI6's network with a direct connection to his personal work machine. And then they wondered why Silva was able to hack them in the first place...
As you've probably discovered, whenever you're dealing with a foreign object on a network, the best way to deal with it is to keep it quarantined. Whether that means ignoring spam emails or trying to open them in a virtual environment is up to you. Personally, I'd opt for the former.