Yes, that's possible, though yours is rather formal-sounding, except for 'grips,' which is not very good with 'heart.'
Heart-rending is also okay, or heart-wrenching; maybe something like
That's what's so moving, even heart-wrenching.
That's what's so moving, so terribly sad.
That's what really gets to you, really wrings your heart.
But really, the two parts of the sentence seem to refer to the same emotion, so it's probably better just to pick one expression, not two. Otherwise there may be a mismatch, because 'moving' or 'touching' suggests only mild to moderate emotion, but heart-wrenching or just sad is much stronger.