I believe yes, Amir hossein Aref it depends on what/which molecule you are considering. As for example if we consider weaker bonded CH3CL, in which C-Cl specifically. Then we can calculate the energy require to break this bond. Like for 9 debye the breaking energy lies near about 3.5eV.
So theoretically you can break these like weaker bonds using electric/magnetic force, And if you can build a machine which such capabilities you can also practically break these type of bonds.
You say a π bond between a solute and a magnetic solvent. You would have to give an example, but a π bond implies a covalent bond and you cannot pull chemical bonds apart. Even if you could exert sufficient force on one end of the molecule, what is holding the other end in place? The whole molecule would move. You also have to explain what you mean by a magnetic solvent. I have no idea what solvent you could be thinking of that will move preferentially under a magnetic field, let alone form π bonds with solutes.