Yes, it is possible to delete or block cookies on a specific website by turning off cookies in your browser settings.
However, turning off cookies might result in a less user-friendly experience, and on some websites, it is more or less impossible to do anything when the cookies are turned off. This can be the case on for example web shops and self-services pages where cookies are used for saving your items in the shopping basket or for remembering your login. Therefore, it is not always a good idea to turn off cookies.