You can achieve this by clicking on a resource and hitting toggling the "power button" to off for each of the resources you don't want to include in the build.
In other tools, hitting re-run would simply replay the job, with the same state it was executed in the first run. I would expect concourse to behave similarly, but no.
If the job failed, you get this. Otherwise I figure that the idea is that you're satisfied with those versions of the resources acted on by the job.
Disclosure: I work for Pivotal.