I had the same problem, which started immediately after I replaced Norton IS with Avast IS. Besides the stuttering, I noticed that the percent of CPU cycles uTorrent was using had gone way up, from the usual 0%-2% range to consistently 25%-35% and higher.
First I shut down the P2P Realtime Shield. Didn't solve the problem.
So following lukor's advice to shut down the Avast firewall, I exited uTorrent and waited for it to truly stop running (looking at Task Manager to see when uTorrent.ext dropped off the list of running apps). I turned on Windows Firewall, then turned off Avast's firewall, then started uTorrent again: absolutely no problems now. No stuttering at all, and uTorrent CPU cycles back down to the normal 0%-2% range. Killing Avast firewall solved the problem (and maybe having killed the p2p Shield beforehand also helped).
Thanks, lukor!!!
Funny thing is, looking on the web before I found this answer, I saw reports of problems with Avast and torrent programs going back to at least 2005, and specifically with uTorrent and the firewall to 2008, and explanations that it's not uTorrent specifically but just that some components of Avast are too slow to keep up with frequently changing connections and event logging, which are common to all bittorrent programs (and that explanation comes from Avast customer service). The problem's been known for years and Avast hasn't bothered to fix it.