I am having the same issue.
Any "cut" action (via ctrl+x, shift+delete, Edit > Cut) results is loss of responsiveness for the cursor for roughly 5 seconds. In fact, if I use the arrow keys to move to a different line during this time (indicated by the margin highlight rather than frozen cursor), the cut action applies to whichever line I end up on rather than the line / lines where the cut action originated. There is no error output in the console (actually the console reports the cut action immediately as shown in a video in one of the earlier comments), and I think it's relatively safe to say it's not caused by conflicting packages because I am using a fresh install.
As many others have said, this makes the editor essentially unusable, and I would love to hear of a fix. Can anyone verify whether or not this issue is fixed in Sublime Text 3 beta?
Running Ubuntu 11.04 32-bit w/ XFCE.
For now, I've gotten things to work sub-optimally using the workaround mentioned by stestagg (combination of installing parcellite & killing xfce4-settings-helper).