You could temporarily deactivate the activity story plugin related to what you are importing. Let's say you are adding new community members to the site. You would:
1. Go to Site Administration > Manage Plugins > Find the 'Joining Users Activity' plugin
2. Click the checkbox to deactivate it and Save
3. Do your import
4. Reactivate the plugin
Also, one of the cool things about the new activity story plugins is that many of them support grouping. For example, in the 'Joining Users Activity' plugin options you can set the time span in which to group join events into a single story. The choices are Day or Hour. You could set that to Hour and then the activity stream wouldn't be so cluttered with a story for each new user...you'd see something like "15 people joined the community" in the last hour.
If it's other content that you are importing (lke blog posts), take a look at the plugins list and find the activity story associated with that. Activity story plugins have "Activity" in the plugin title.
Hope this helps!