You can cut your opponent's support by also attacking the unit which is giving the support.

For example, France has an army at Brest and an army at Paris. He orders Paris to move to Gascony with a "support move" order from the Brest army. England meanwhile has fleets at Spain (North Coast) and Mid-Atlantic Ocean. If the Mid-Atlantic Ocean fleet attacks Brest, he will not capture Brest, but he will prevent the Brest army from giving support to the move from Paris to Gascony.

Does that answer your question?

No I have a more difficult issue:
http://webdiplomacy.net/board.php?gameID=49687&msgCountryID=0&rand=93847#chatboxanchor
I want to prevent Paris from being invaded by the German's by sending an army from paris to Burgundy, so burgundy can't move into paris or support move picardy if he wants to invade paris from picardy. By moving my Brest army to picardy I can keep picardy from moving into paris or from supporting burgundy. Now I wanted to move both armies because I also want to protect Gascony from the germans. But I want to be sure Paris stays at the same spot and doesn't accidentaly move into Burgundy. So if I would also sent my army from marseilles to burgundy, both armies won't move. But will
the armies from marseilles and paris still have effect on burgundy if I move both into burgundy?

Now he knows what you're planning !!

We're not supposed to give you advice about ongoing games, but in terms of this question, I think the answer is yes. You can move two of your armies to one territory. They bounce each other and return to their starting positions.

But will it prevent the enemy's country moving?

You will cut Pari's support but depending on the strength of Paris' move you may or may not stop that.

Bounces can cut support, but nothing stops a move other than insufficient force to take the territory it is moving to.