When the Yom Tov of Rosh HaShanah falls out on Shabbat, the shofar is blown in the Beit HaMikdash, but not in the Medina [the synagogues in the cities and towns]. (Rosh HaShanah 29b)
R' Avraham of Slonim, the Beis Avraham, explained that all mitzvot exist in the realm of thought and intellect as well as in the realm of active, physical application. The intellectual realm is referred to as the "Mikdash", while the active, physical realm is called "Medina".
When Rosh HaShanah falls out on Shabbat, the shofar is sounded in…an internal fashion…
When Rosh HaShanah falls out on Shabbat, the shofar is sounded in the Mikdash, but not in the Medina. We sound the shofar in an internal fashion, but without the actual shofar. The intentions underlying the shofar are realized only in the internal aspect. When Rosh HaShanah falls on Shabbat, the blowing of the shofar is a sublime, spiritual action which must take place in the inner recesses of one's heart, and in the depths of one's soul.
Blow the shofar on the day of new moon... (Psalms 81:4)
In Hebrew, "Tiku ba'chodesh shofar, ba'keseh l'yom chagainu", literally "Blow the shofar when the moon is covered", i.e. when the moon is small, on the 1st day of the month. The acrostic of the verse contains the letters tav, beit, shin, beit, which, when rearranged, spell "B'Shabbat" - "on Shabbat". On Shabbat the blowing of the shofar is in a covered, hidden way. One may still reach the deepest levels of the mitzvah of shofar, yet without the actual shofar. They are accomplished in a hidden place; in one's heart and through one's intentions.
Happy is the nation that knows Terua [the shofar blast], they walk in the light of your countenance, G‑d. (Psalms 89:16)
The Zohar (III, 233b) points out that the verse doesn't state, "happy is the nation that hears Terua", or "happy is the nation that blows "Terua", but "happy is the nation that knows "Terua". They know the secret of the Terua, as it is written, "Shatter (in Hebrew, "Teraim") them with an iron rod". (Psalms 2:9) Terua is derived from the root "to break" or "shatter", hence the broken notes of the shofar.
The first day of the seventh month shall be a sacred holiday to you when you may not do any mundane labor. It shall be a day of Terua for you.(Num. 29:1)
The Torah instructs us how to sweeten and break the severity of any judgment pending against us on Rosh HaShanah. ". . .it shall be a day of Terua for you." When Rosh HaShanah falls out on Shabbat, a Jew must make it a day of Terua in its inner dimension. A Jew must shatter his stony heart into pieces until his ego is completely nullified and he can honestly declare, "I, and everything that I possess is for G‑d alone".
The Zohar speaks about a watchman who points out each Jew to the heavenly court, "This one did this mitzvah, and this one committed this transgression". But when a Jews appears before G‑d with a broken heart, his ego erased and his only desire to do the will of G‑d, then there is no "one", no individual who can be accused of any transgression. The severity of the judgment has been sweetened and has nowhere to make itself manifest.
(First published in B'Ohel Hatzadikim, Rosh Hashanah 5760)