Among Cubans, to be called a ''Marielito'' has become an insult. Some 120,000 people streamed aboard boats in Cuba's Mariel Harbor three years ago to escape to Key West. Many sought escape from the communist regime of President Fidel Castro and hoped to be reunited with family members in the United States. But others were violent criminals, mental patients, political dissidents, and vagrants who were forced by Mr. Castro to leave the country.
''For me to call you a Marielito now is a disgrace,'' said one leader of Tampa's Cuban community. ''It has come to mean the worst of the worst.''
But many Spanish-speaking residents stress that the national attention focused on the worst of the boatlift refugees overshadows the accomplishments of the majority, who are hardworking people trying to get ahead.
The refugee community in Tampa, numbering 5,000 to 10,000, is an example of the progress being made by the refugees as they move to cities throughout Florida and the US and begin adapting to American society.
Looking at the city's boatlift population after three years in America, one sees:
* Students of all ages who are learning English and basic skills and working toward high school equivalency diplomas in classes run by a combined state and county program. They talk about becoming computer operators, nurses, and mechanics.
* A jewelry shop in a predominantly Latin section of town, run by a Mariel entrant who is following the path of Cuban refugees in the 1960s who worked their way into the American mainstream by starting out in small retail businesses.
* A rocking chair, once used frequently by the principal of an elementary school to comfort children who were emotionally upset from being uprooted. Now it's hardly needed, and the number of bilingual teachers at that school, which was flooded with Cuban pupils after the boatlift, has been sharply reduced as the students learn English.
Undoubtedly, however, the refugees' transition is not without grave problems. In Tampa, scores of families are still looking for jobs, food, and clothing at a church-run refugee center, after three years of trying to adjust to America.
And there are other incidents that add to the ''Marielito'' image. Police here say a grocery store owner was killed by a vicious, hard-core criminal sent to the US from Castro's prisons.
Boatlifted Cubans account for about 14 percent of the murders committed in Tampa during 1981 and '82, police statistics show. ''Those people are extremely violent,'' said one Spanish-speaking detective who has interviewed many of the murder suspects. ''They have no morals, and they lie and lie and lie.''
He says the problem is growing ''because they are starting to understand our laws. They know they are a hundredfold safer here than in Cuba, because here they have rights.''
While police deal with the criminals, welfare agencies try to help illiterate and unskilled workers. Relief officials say two decades of communism have destroyed any work ethic the Cubans may have had.
''In Cuba, they were absent all the time from work, because they knew there was no advancement outside the Communist Party,'' says a Lutheran refugee worker. ''Here, if you work hard, you have a chance to advance, but they don't understand that.''
But many have decided to work hard.
''My father saved me,'' said an auto mechanic who has worked continuously since arriving in the US. ''When I was growing up in Cuba, he told me to stay out of trouble, but don't believe the propaganda. He told me this was no life for me, and when the boatlift offered the opportunity, I was ready to leave.''
A government-run program offers Mariel refugees $1.75 an hour if they will study English and learn basic skills for living in America. The offer has attracted hundreds of students, who the instructors say are seriously studying toward high school equivalency degrees so they can go to trade schools.
''If I want to get a nice job, I have to learn English,'' said one student.