The legislative branch is in charge of deciding the rules. The executive branch is, as the name says, in charge of executing those rules. If Congress wishes to end a war, they can simply pass a bill doing so. This would be subject to the president's veto power, so if the president is determined to continue the war, Congress would need 2/3 majority in both houses. If you want textual support, there is plenty in Article I, Section 8. For instance:
The Congress shall have Power ...
To make Rules for the Government and Regulation of the land and naval Forces;
So they can make a rule that the land and naval forces can't participate in the war (I suppose there is a bit of a loophole regarding the air force, but I think most judges would find that to be included).
To define and punish Piracies and Felonies committed on the high Seas, and Offenses against the Law of Nations;
The Congress can declare the war illegal and punish anyone participating in it.
To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water;
The Congress can prohibit any capturing, which would make prosecuting a war more difficult.
To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;
The power to support the army suggests the power to have it not be supported.
To provide and maintain a Navy;
This implies that the power to maintain a navy is Congressional prerogative, and they are free to, for instance, disband it if they wish.