There are many reasons why you may want to remove a User/contact from a WhatsApp chat group; contact has become abusive, vulgar, unfriendly, not beneficial to the betterment of the group, feedback they are providing is not is the interest of the group, contact has had their phone stolen and the group information is sensitive.
Mind you this will only stop them from receiving further chats, and NOT delete the previous chats that they received from the group.
In order for you to delete Users/contacts to existing WhatsApp groups, you need to be the Group Admin. If you are not the Group Admin, get in touch with them and forward them the contact that you would like to delete.
To delete a contact from an existing WhatsApp group simply do the following:
1. Open WhatsApp
2. Click on the WhatsApp group where you would like to delete the contact
3. Click on the title at the top
4. Scroll down to the name and number of the participant/s whom you would like to delete from the Group
5. Click and hold (for touchscreen users, I'm not sure on those with a keypad) on the participant's name and number
6. Select "Remove CONTACT from the group" and you're done.
Remember it is common courteous to ask, or advise all group members that you are deleting someone from the group, as well as advising the contact whom you have deleted why you have taken such action.