Here's a way that uses a data step. This method requires a sort.
data person_groups;
input person $ group $;
datalines;
John Grp1
Mary Grp3
Joe Grp2
Jane Grp3
Frank Grp1
;
Proc Sort data=person_groups;
by group;
run;
Data person_groups;
set person_groups;
by group;
if first.group and last.group then delete;
run;