Can an employer, cut my salary without notice even after signing an agreement?

First, you need to have an attorney review the agreement, to see if it formed an enforceable contract--in which case, they could only reduce your salary in compliance or accordance with its terms; and if they violate its terms, you could sue them, for "breach of contract," for compensation. Not all "agreements" signed by an employee at work form an enforceable agreement--some are just informational, informing the employee of the current position, salary, benefits, etc. without obligating the employer. Whether it forms an enforceable agreement or not will depend on its specific language of the agreement and whether there was sufficient "consideration"--something of value, including you potentially working additional hours, or different shifts, etc.--given by you to the employer. (If you did not provide consideration, then this was just a "gratuitous," or freely given and unenforceable, promise, not a contract.) So let an attorney review the agreement and facts and see if you have something enforceable. 
Second, though, if you worked under the new, lower pay for a long time--more than year, as your question states--that may be taken to be your agreement to the lower pay. People are not allowed to "sleep" on their rights"; if you don't enforce your rights under an agreement, but instead demonstrably accept a change in the agreement, that can often prevent you from, at a later date, enforcing the agreement. A court might conclude that you agreed to keep working for less, because you did keep working for less. This is something else to discuss with an attorney.