It is impossible for a person to remove all desires. But we have the ability to channel our desires from physical and material pleasures to spiritual endeavors.
This is analogous to a person who went to a fancy restaurant where two full plates of food were presented to him. One was full of fish and the other was full of meat. There was too much food for him to eat both dishes. Since he liked fish better, he chose the fish and pushed the plate with meat to the side.
Another person walked by and looked at him with amazement. The second man, who liked meat much more than fish, thought to himself, "How could this person who has a plate full of delicious meat decline to eat it?" The second person made a mistake. The first person was not overcoming a desire to eat meat.
Rather he was gratifying his desire for fish, which he enjoyed more than meat. Similarly, someone who finds fulfillment in spiritual matters is not being deprived of pleasure. Rather he is gaining more pleasure than is possible in material matters.
(Ohr Yohail, vol.2, p.27; Gateway to Happiness, p.359)