oh no that’s not true! there are a lot of puns in ASL! they are not English puns so its different. you have probably heard of the popular ones (or maybe not if your teacher thinkgs there are none) but there is the “pasteurized milk” one which is more englishy it’s where u sign MILK passing your eyes so it’s: past your eyes milk. another popular one is a joke i hear a lot of ASL students learn is where Deaf king kong climbs up the building and kidnaps the lady and tries to say “i want to marry you” and crushes her when he signs MARRY. Or the microwave one where you do a little wave with your pinky finger and it is a “micro wave”, which is also like if you only understand something a little, you can sign UNDERSTAND with pinkie finger instead of pointer finger. another one i recently learned is the sign for the city El Paso, you make a L with dominant hand passing by an O with nondominant so it is “L pass O”. another one is doing sign for CHEAP with a W to mean walmart which i have not seen a lot but still pretty good. you can sign FOREVER with an ILY handshape to mean “I love you forever” I guess that is sort of a pun. name signs can also be puns sometimes for example i have a friend name Brenda who has very long eyelashes and her name sign is a B signed in front of the eye and flutter up and down like eyelashes. something me and my friends do a lot that i guess is like a pun is sign PLAY in front of the eyes to mean “we’ll play it by eyes” instead of “we’ll play it by ears” when deciding on making plans, so that is just a Deaf joke i guess haha
anyway those are the ones i can think of of the top of my head. mainly i guess ASL puns are not like english puns bc they’re 2 different languages so its not the same style. its more like playing around with signs and where they are made and stuff i guess but yes they are there in ASL!