I uploaded a changeset from sandbox to production. If I delete the change set in the source org, should it still be available in production? What will be the effect of deleting the changeset in the source on destination.
The two orgs are independent of one another. Deleting change sets in your sandbox will have no affect on the change sets that have been uploaded to your production org.
Assuming no relevant changes have been made in your sandbox, a change set that's been deleted could be re-created at a later time. Otherwise, it would come down to an issue of version control, if that at all applies to your situation.
Its not unusual to have a change set that installs a new trigger and another change set that turns the trigger off; thus restoring the production org to it's original condition. As development progresses on the new trigger, one might want to delete earlier versions of the change set that installs it since they'd be of no use in the future if that version of the trigger contained bugs.