Language
Deaf people use profane or dirty words the same way hearing people do. As expected.
Possibly, the best way to learn some cuss words in ASL is to have Deaf ASLian friends. Of course, you can google them too (maybe).
Language and culture
The middle-finger gesture is understood as not from ASL. It is said to be the origin in wars or ancient Rome. Another, the gesture for "bullsh*t" (dominant-handed 'horn' handshape on the left elbow while the passive hand is on the right elbow) is said to be not part of ASL. But, the handshape had found its way into ASL.
There are some signed words used to curse, while few of those are not exactly cuss (or gray-area) words, such as the middle-finger handshape that became part of a word that can convey other meanings rather than the conventional gesture. Occasionally, the middle-finger handshape can be found in a few non-cuss words (signs).
For example, when a Deaf/ASL-speaking person used that particular inflected 'middle-finger' signed word in a sentence, sometimes some interpreters and signers mistakenly translated it into English 'f*ck'. But, that signed word in context is, in fact, interpreted as RIP-OFF or other related meanings. This mishap had happened in interpreting.
Deaf people are so creative with ASL language. One example is the blend of the middle finger with a signed word such as UNDERSTAND and HEARING used in particular situations.
One of some perks about being Deaf is that one can swear at the same time have a happy smile on their face without anyone (non-signer) knowing. Not limited to cussing, this is especially true when an angry Deaf parent can utter a warning (no cuss for clarification) with a happy face to their kid(s) without anyone (non-signer) understanding.
"Whenever I tell someone that I'm studying American Sign Language, there is a nonzero chance that they'll trot out the same tired joke: 'Oh yeah? I know some sign language! [Flips me the bird.]' They laugh, and I laugh, and we promptly stop being friends. Really, though, these people have no idea just how right they are. It's only that, when you're talking about a language that has spent hundreds of years figuring out how to squeeze the absolute most meaning out of every part of a hand, merely throwing up a middle finger is the linguistic equivalent of showing up to a duel and then firing your pistol straight into the air." -- Stan Carey (2017)
Similarly, in this video below (1:30), the hearing guy tried to impress his date, "Oh, they are deaf? ... Actually, I know one sign." The woman was impressed, "Oh yeah? What's that?" He showed the manual gesture (not signed word, mind you) "bullsh*t". That ensued the rest of the story.
What is the sign for (cuss word)?
Another cultural aspect to be aware of is when one asks a Deaf person to show a sign for a taboo word.
One of some experiences is that a certain group of hearing people only wanted to learn dirty words. Or, sometimes they first ask how to sign a few words then later ask for showing them how to sign cuss words. We have been asked at times in our lifetime.
What does a Deaf person do or feel when a hearing person asks? One might not mind. Or another might respond, "If you want to know, go to ASL classes."
Of course, ASL instructors don't teach nor show when asked. The meanings behind this suggestion or comment are several.
"You don't care to learn about our language and culture. We're not gonna please you. Is that all you care about?"
Why? What's the big deal about it? Try to understand this in our shoes. As an oppressed group, we've been dealing with hearing oppression and ill-mistreatment for a very long time. "Interested in cuss signs? Get out." It's a hearing privilege.
Or, some nicer variants of "When you socialize with ASL/Deaf speakers, you'd pick up a few. You have to earn it." In other words, learn sign language.
Real-life scenario: A visiting artist gave a presentation at a college of art and design. At times, during his presentation, he used some dirty words. Next to him was an interpreter in front of me. At one point, as the artist uttered dirty phrases and dramatically turned around and looked at the interpreter, the interpreter instinctively knew the intention and interpreted fast with euphemisms. She was done just in time and looked straight with her hands resting on her lap. The artist looked, not seeing anything, and turned his head toward me. I smirked and shrugged with raised eyebrows, signing "You missed it" (translated back via the interpreter). The artist students in the audience laughed. (I appreciate the fact that the interpreter did nothing, only faciliating, leaving me to respond.)
A Deaf person once had a hearing friend who wanted to learn ASL from her but wanted to sign with more cuss. She/he asked other Deaf people and signing hearing allies for their thoughts.
"I won't teach people who only want to learn to swear. Respect the language or don't learn it at all."
"Literally she's wasting your time."
As always, there is a difference in view: "Teach her vernacular, what you and she say, learning language by using is best. If she cusses all the time, then that's what she needs to learn."
No university student in my ASL classes has dared to ask me (maybe unless they were high school kids). Except for one, a courageous student asked me whether I'd show how to sign a cuss word. I told her, "It's not part of the curriculum. You'd have to earn your way into Deaf community."
"Darn!"