Exodus 21:10-11 says “If he marries another woman, he must not deprive the first one of her food, clothing and marital rights. 11 If he does not provide her with these three things, she is to go free, without any payment of money.” Does this mean that if a husband does not provide food or clothing for his wife, or if he sexually denies her, that his wife can divorce her husband?

No. Exodus 21:10-11 is specifically written in the instance of a man who has two wives, not a man with one wife. 

1 Corinthians 7:2 – But because of sexual immoralities, each man is to have his own wife, and each woman is to have her own husband.

To the man with one wife, the Apostle Paul says:

1 Corinthians 7:3-4 –  The husband must fulfill his duty to his wife, and likewise the wife also to her husband. 4The wife does not have authority over her own body, but the husband does; and likewise the husband also does not have authority over his own body, but the wife does.

Paul does not consent to sexual denial in a marriage on either the wife or husband’s part. That being said, he does not allow sexual denial to be a reason for divorce for neither the husband nor the wife. 

1 Corinthians 7:10-11 – To the married I give this command (not I, but the Lord): A wife must not separate from her husband. 11 But if she does, she must remain unmarried or else be reconciled to her husband. And a husband must not divorce his wife.

Paul specifically states that the commandment of a wife not divorcing her husband for any reason is not from himself but rather from Jesus.