Can my employer stop me from working for a competitor?

Yes, a noncompetition agreement is legal and your employer can require you to sign one, or terminate you. Generally, however:
1) They are generally only enforceable if you quit/resign or are fired "for cause" (for wrongdoing); if terminated not for cause, they would only usually be enforceable IF you received some separate payment, bonus, or benefit, other than simply having your job, in exchange for signing. That is because the noncompetition agreement is generally an agreement that in exchange for having a job, you will not compete; if they terminate you when you did nothing wrong, they have breached their obligation under the agreement and that breach lets you consider the agreement to be terminated. Also, all contracts need "consideration," or something of value, exchanged between the parties to bind them. The consideration the employer gives the employee is employment; take that away involuntarily and without good cause, and there is no consideration.
2) Even when courts enforce non-competes, they can "blue pencil" them to reduce terms that are excessive, unfair, or unnecessary for the employer's protection. Typically, 2 years is longer than would be enforced vs. a non-executive, senior sales person, or (former) owner employee; usually, 6 months to 1 year is an enforceable length. So this contract could be reduced by a court if challenged.