When a person's hand or speech becomes an instrument of God's will, it does not mean that it is the organ itself that is thus being used; God is acting through the person as a whole.
However, when a person studies Torah, with mouth and mind, he reaches a deeper and more internalized relation with God.
Because there is a certain difference between the mitzvah and Torah study.
The performance of the mitzvah is a means of expressing and fulfilling whatever God wishes to happen in the world.
When my hand gives alms, it means that God desires to sustain this needy person.
I am only a means of accomplishing this.
If God wishes someone to wear tefillin, my hand and head serve to realize this.
If He wants the Chanukah candles lit at a certain moment, my performance of the mitzvah assures that His will is done.
However, when a person studies Torah, there is a more profound factor involved, for the Torah itself is God's will.
Thus, for instance, when one studies a Halachah, the way of Torah, about the performance of a ritual, such as the lighting of the Chanukah candles, and it becomes apparent (through study) that a source of flame that is fed like a bonfire is not a proper Chanukah candle, one is taking part in the idea behind the ritual as well as performing it.
One is identifying with the Divine Will in the matter and not only obeying it.
By becoming involved in the reasons for the action and the correct way of doing it, one is raised to a higher level of functioning, like one who reads the plans for a building under construction and does not merely lay the bricks.
–Rabbi Adin Steinsaltz
From The Long Shorter Way by Rabbi Adin Steinsaltz