I am running PeopleTools 8.61.x, HCM 9.2 but this should be possible as long as you can make a SOAP call out from PeopleSoft.
User Groups are part of the UserAccount construct as shown below. Following is a simple construct to pull up or search for an user account and then assign a user group to the user account.
<UserAccount>
<Loginname searchType="search" searchTarget="../../.." searchValue="user@emaildomain.com" />
<Groups>
<Group>
<Name searchTarget="." searchType="search" searchValue="Group-Code-01" />
</Group>
</Groups>
</UserAccount>
To delete all the User Groups assigned to an user the request XML will be like below.
</UserAccount>
To delete only a specific user group from the list of assigned user groups on an user profile the request will be like below.
<UserAccount>
<Loginname searchType="search" searchTarget="../../.." searchValue="user@emaildomain.com" />
<Groups>
<Group action="remove">
<Name searchType="search" searchTarget="." searchValue="Group-Code-01" />
</Group>
</Groups>
</UserAccount>
One can combine the above actions in a single request like removing all or one user group and assigning a new user group.