What happens when you delete someone on Snapchat

They will not see your snaps

As soon as you delete the other person on Snapchat, all the stories you have posted will not be seen by the person you have removed as the person is no longer available to see your stories.
You will not see their snaps

The stories posted by the person whom you have deleted will not be able to viewed by you.
They can still message you

The person whom you have removed will still be able to send you the message on Snapchat.
They can still send you snaps

Anyone can send you their snap even if they are unknown, or that person was your former friend on Snapchat whom you have deleted now.
A pending status will appear

Whoever will send you the snap, be it an unknown person or the person you have deleted, will find a ‘pending’ status until you let them add again and see the snap they send you. (See What happens when you delete a friend request on Facebook?)
Their username will disappear from your contacts

You will not be able to see the deleted person’s name in your Snapchat contacts.
They can only see your public stories

Unless you add the person as public and set your stories settings as viewed by the public, the person will not see the stories posted by you. (See Why do people like Snapchat?)
They will not receive a notification

Your deletion will not notify the person you have deleted.
They can add you again

The deleted person can still send you the request again to add them back.
They will not be notified if you add them again

If you have deleted a person over snapchat and added them again, they will be notified of becoming friends with you. In this case, they will get to know that you deleted them in the first place, as that is why you have to add them again.
They will see the saved messages

The person you have deleted will still see your messages only, which they have saved in your chat.