I receive the Eucharist every Sunday; however, should I do so if I have an unconfessed mortal sin on my conscience? A priest told me as long as I am actively trying to eliminate this sin from my life, the Eucharist is helpful, and I shouldn't deprive myself of the grace present in the Eucharist. He said if I stop trying to eliminate this sin, then don't present myself, but as long as I'm trying, don't deny the Eucharist to myself. Is this good advice?
Three requirements must be met for sin to be mortal: grave matter, full knowledge, and deliberate consent. Since you say that you are "actively trying to eliminate this sin" from your life, your priest may believe that your action lacks deliberate consent and, therefore, does not qualify as mortal sin. If this is the case, the Eucharist may benefit you greatly. On the other hand, if your sin is indeed mortal sin, then you should not receive the Eucharist without first going to confession.
The Code of Canon Law is clear that a person conscious of mortal sin may only receive the Eucharist under grave circumstances:
A person who is conscious of grave sin is not to celebrate Mass or receive the body of the Lord without previous sacramental confession unless there is a grave reason and there is no opportunity to confess; in this case the person is to remember the obligation to make an act of perfect contrition which includes the resolution of confessing as soon as possible. (CIC 916)
The Catechism of the Catholic Church explains,
The Lord addresses an invitation to us, urging us to receive him in the sacrament of the Eucharist: "Truly, I say to you, unless you eat the flesh of the Son of man and drink his blood, you have no life in you." To respond to this invitation we must prepare ourselves for so great and so holy a moment. St. Paul urges us to examine our conscience: "Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of profaning the body and blood of the Lord. Let a man examine himself, and so eat of the bread and drink of the cup. For any one who eats and drinks without discerning the body eats and drinks judgment upon himself." Anyone conscious of a grave sin must receive the sacrament of reconciliation before coming to Communion. (CCC 1384-1385)
I recommend that, after engaging in grave matter, you go to confession as soon as possible and then receive the Eucharist as often as possible. "By the same charity that it enkindles in us, the Eucharist preserves us from future mortal sins. The more we share the life of Christ and progress in his friendship, the more difficult it is to break away from him by mortal sin" (CCC 1395).