create table foo;
create table foo (id text, name varchar(15));
insert into foo values ('a','foo');
insert into foo values ('b','foo');
insert into foo values ('c','foo');
create table backupfoo (id text, name varchar(15));
insert into backupfoo (select * from foo);
delete from foo; -- you would obviously use a WHERE clause to restrict what you are deleting
>>> 3 records copied
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pg_dump -d YOURDATABASE -t backupfoo > mybackup.sql
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psql -d YOURDATABASEARCHIVE -f mybackup.sql