The Gemora states that a positive commandment can override a prohibition that carries with it a standard punishment.
The Gemora provides an example for this: The positive commandment of performing circumcision overrides the negative commandment of cutting off tzaraas.
My brother, Reb Ben cites the opinion of Rabbeinu Nisim Gaon, who writes the following: Many people cast doubt on this precept, as we know that a negative commandment is more stringent than a positive commandment, so why should a positive commandment supersede a negative commandment? Rabbeinu Nisim answers that a positive commandment is set, and if there is a negative commandment, the negative commandment only functions if there is no contradiction to the positive commandment. This is what Hashem decreed, that the positive commandments remain in place, and the negative commandment only functions if there is no contradiction to the positive commandment. The Ramban , however, writes that the reason a positive commandment supersedes a negative commandment is because in reality, a positive commandment is greater than a negative commandment. A positive commandment is a reflection of the love Hashem has for us, because one who fulfills the instructions of his master is beloved by his master and the master will have compassion on him. A negative commandment, however, is a reflection of Hashem’s Attribute of Judgment, and stems from fear. Since love is greater than fear, the Torah states that a positive commandment supersedes a negative commandment.
Based on this premise, the Meshech Chochmah explains that one who violates a negative commandment deserves a greater punishment than one who does not fulfill the will of Hashem. Nonetheless, since it is the will of Hashem that one observes both positive and negative commandments, one who fulfils a positive commandment demonstrates his love for Hashem. One who does not violate a negative commandment, however, merely demonstrates that he is afraid and nothing more. For this reason, the torah states that a positive commandment supersedes a negative commandment. An example of this is one can wear Tzitzis with Techeiles on a garment of linen, as the positive commandment of wearing Tzitzis supersedes the negative commandment of shaatnez. The reason for this is that one who wears shaatnez does not transgress the will of Hashem. In fact, the opposite is true, as by donning Tzitzis, he is fulfilling the will of Hashem.
In regards to the question: Why is it that a positive commandment overrides a prohibition and yet the punishment for transgressing a prohibition is much more severe than the punishment for not fulfilling a positive commandment?, Reb Yossie Schonkopf said over a parable from his Rebbe: A trucker is hired to transport a load across the country and the owner warns him not to go beyond the speed limit, not to crash the vehicle and to follow all the road instructions. If the trucker does everything perfectly but doesn't unload the goods at his destination; rather, he arrives at the destined location and immediately turns around carrying the same load, what is accomplished by the fact that the trucker obeyed the speed limit and followed all the rules?
The meaning is as follows: Our mission in life is to accomplish in this world and 'build the love towards HaShem,’ therefore, this building overrides the transgressions. The prohibitions are only there to protect what has been built and not to suffocate the building.
This concept is elucidated by the Ramban in Parshas Yisro. He states that the fulfillment of a positive commandment is based on ahavas HaShem, loving HaShem and refraining from committing a transgression is based on yiras HaShem fearing HaShem. It is a higher level to serve HaShem through love, but it is worse to violate a prohibition, which is based upon fearing HaShem.
My brother, Reb Ben asked a similar question: The Gemora states that a positive commandment will override a negative commandment when both commandments are performed simultaneously. It is noteworthy that the Gemora in Sota states that a mitzvah cannot extinguish an aveira, a sin, yet an aveira can extinguish a mitzvah. Apparently, the principle that a positive commandment can override a negative commandment is not a contradiction to this Gemora. Perhaps the idea is that when one performs an aveira intentionally, he has rebelled against HaShem, and it is not possible for one to appease HaShem with a mitzvah when he has just committed an act of rebellion. When one is simultaneously overriding the negative commandment by performing a positive commandment, however, he is demonstrating that he is fully aware that he is performing a negative commandment, yet he is permitted by the Torah to override the negative commandment. This principle allows him to perform the positive commandment and be rewarded for its performance.