Why is my MacBook Pro (late 2013, Retina) crashing?
Started as a comment, but got too long. You are asking two questions. The "spinning beach ball of death" and the crashing MailServiceAgent are most likely unrelated.

To clarify. The "spinning beach ball of death" doesn't actually indicate that anything is crashing. It indicates that an application (most of the time, temporarily) is not responding to messages from the operating system.

From Apple's Human Interface Guidelines:


  The spinning wait cursor is also standard, but it is displayed
  automatically by the window server when an app can't handle all of the
  events it receives. In general, if an app doesn’t respond for a few
  moments, the spinning wait cursor appears. If the app continues to be
  unresponsive, users often react by force-quitting it.


If you move the cursor around, does the wait cursor still appear if it is over another application or over your desktop? If you ALT+TAB to bring another application to the foreground do you still get the wait cursor? If it only appears over one application then that application alone is having an issue. If it appears over all applications or if you find you are unable to move the cursor or to ALT+TAB to another application then you have a wider system problem rather than a problem with one specific application.