Low space on disk 

The most common cause of this problem is that you are low on disk space. If your hard disk is 90% full or higher, OS X begins to have some performance issues in general, but it especially affects the overhead required to launch new processes. Since SourceTree relies on launching Git/Mercurial (hg) and other processes regularly, running out of disk space adversely affects it.

SSD drives seem to be particularly affected.

Repository run on a remote drive

Another possible cause is that you're running the repository on a remote drive, such as a NAS. This is not a recommended configuration, and it can actually cause other issues, such as corruption in Git if you're using a Windows (SMB) share (note that this is a problem related to Git and not to SourceTree).

Free enough space on disk

Clean up your hard disk so that you're consistently running at below 90% utilisation

Repository run on a local drive

Move your repositories so that it runs on a local drive