See also the official documentation:
Help Center > Group Owners Manual > Managing members > Moderating individual members

Moderating an Individual Member

Many of us want free and open conversation between our members and go with the default setting of moderating only a new member's first post as an anti-SPAM measure.

Sometimes however, there is a member who just doesn't always play nice.

What's a moderator to do? You don't want to change the rules for anyone but this person ...

How to Moderate an Individual Member

NOTE: Moderators have the ability to edit messages to remove unwanted content. At your option you can add a moderator's note explaining what you did.

Method 1 - Available to both Free and Paid groups

1. On the left navigation menu, click Admin.
2. Click Members.
3. Click the offending member's email to pull up the member's profile.
4. Scroll down to the bottom to Posting Privileges. By default, "Use Group Moderation" is selected.
5. Select the level of moderation you deem appropriate.
   NOTE: If they are only out of line occasionally or need minor adjustments, Override: moderated is probably the right choice.
6. Click Save.

Method 2 - Paid groups only

1. Click the offender's name in a message.
2. Click Profile in the header bar.
3. Scroll down to the bottom to Posting Privileges. By default, "Use Group Moderation" is selected.
4. Select the level of moderation you deem appropriate.
   NOTE: If they are only out of line occasionally or need minor adjustments, Override: moderated is probably the right choice.
5. Click Save.