Emoticons and emoji replacements can be managed by going to Administration > Site > Emoticons:
Emoticons are grouped into categories. Each category contains one or more emoticons which can have variations (for skin tone, for example, as is the case with emoji).
Emoji and Emoticons
The default categories mirror the groupings of emoji characters which are part of Unicode. Emoticons and emoticon categories that relate to emoji/Unicode can be enabled/disabled but cannot be removed. Disabling a category or a single emoticon within a category related to emoji disables that emoji character from being used in any content within the community. Enabled emoticons related to emoji will replace the emoji character to provide a consistent visual representation of the emoji for all members of the community.