As it happens, grappling and throwing -- including using the sword as a tool for the purpose -- is very much a part of some koryu bugei systems. In those of the Bujinkan, four ryuha I can think of immediately where it's a common feature (for different reasons depending on the ryuha) are Kukishinden ryu Happo Biken, Takagi Yoshin ryu, Shinden Fudo ryu, and Togakure ryu.
It's a major feature of armored battlefield swordsmanship as exemplified by the first one I mentioned above, as frequently the "ideal" clean cuts you'd do in unarmored dueling are not easy to achieve. Since you still need to kill the opponent, what is often needed is to place the edge or point at an opening or weak spot on the yoroi while taking the opponent's balance and push the cut or thrust through; and often this happens "inside" the range of his own sword. (This also is done with polearms such as yari and naginata as well, often outside the range of his sword.) Joint-locking and/or throwing, using the weapon for leverage, is often a part of the cutting action.
Takagi Yoshin ryu contains an entire body of material referred to as daisho sabaki, dealing with jujutsu methods used where both combatants are wearing their swords but the "defender" hasn't yet drawn his as he's being attacked (while the attacker may either have already drawn his or be in the act of drawing). The concept behind this is that in such a situation you have, in addition to your taijutsu or body skills, four swords available to you: both of yours and both of his.