CathInfo.com

“In the encyclical (i.e., Mystici Corporis), the Holy Father speaks of schism, heresy, and apostasy, as sins which, of their very nature, separate a man from the Body of the Church.  He thereby follows the traditional procedure adopted by St. Robert himself in his De ecclesia militante.”
(Monsignor Joseph Fenton, The Status of St. Robert Bellarmine's Teaching about the Membership of Occult Heretics in the Catholic Church, The American Ecclesiastical Review, March 1950, p. 219)

What 'traditional procedure' adopted by St Robert Bellarmine is this referring to?

The public sin of manifest formal heresy per se separates the heretic from the Church.

This is not directed to Catholic Knight specifically, but to everyone on this thread...

In all my years on this site, i've never seen an actual, concrete definition of what "manifest" or "formal" heresy is.  And i've never seen St Bellarmine's definitions used, when debating his actual quotes.  These 2 terms are NOT the same.  These terms are from canon law, which have unique legal definitions.  And over the centuries, some terms are used differently, depending on the time period (i.e. St Bellarmine's days of 1600s vs St Alphonsus in the late 1700s.)

The point is, no one can read a quote from St Bellarmine (or canon law) and just privately interpret what "manifest heresy" means.  It does not mean what you find in the dictionary - i.e. readily understood, obvious or apparent.  You have to go look up the definition AS ST ROBERT DEFINED IT, or AS CANON LAW DEFINED IT.  Because it's a legal term, with a certain, unique legal definition, based on the time period (since canon law has been revised many times) or based on the saint/theologian's personal use.

So as people continue to debate how to apply St Bellarmine's opinions on the pope, or canon law's excommunication rules, you are wasting SO MUCH time (and solving nothing) by using your private-interpretation of these words.

Also, Fr Hesse, who was an actual canon lawyer, has given his opinion on all these matters.  The 'pope heresy' question is not as clear-cut as you think.  The pope is above canon law, which means all those arguments about 'ipso facto' are meaningless.  What's left is the OPINION of St Bellarmine and historical papal docuмents which kindof apply but not exactly.  So what we're left with is a bunch of gray area. 

If the answer were clear, then St Bellarmine (and all the super educated theologians of his day) would've agreed.  If the answer were clear, then Trads of our day wouldn't still be arguing about this 70+ years after the start of the biggest crisis in Church history.

If you want to continue debating, I suggest you start fresh by researching/using the proper defintions by each quote/source you want to use to support your view.