You can permanently delete Snapchat stories by opening Snapchat, clicking Three Dots (⋮) followed by the snap target, and hitting the trash icon while confirming the process. An immediate deletion occurs instantly without any chance to recover it.
Check to see if your Snapchat application needs an update before trying once again to remove the posted story. Tap on your Story then choose the three dots button and select "Delete". Restart the app or device when the previous methods fail to remove the posted story. In case of persistent issues you should reach out to Snapchat Support and review their help center information.
Hey, @ruchii do not get confused in the above recent forum replies. One of the people doesn't give accurate details to you. Consider the below points and delete your Snapchat story as quickly as possible, if posted wrongly.