Most English speakers can correctly infer from the negative prefix dis- that disassemble means the opposite of assemble. Dissemble is trickier because it sort of sounds like it should mean the opposite of assemble, but it actually means (1) to disguise (either oneself or something else) behind a false appearance, or (2) to obscure the truth with showy rhetoric. It’s traditionally synonymous with disguise, but it has become a fancy word for lie in 21st-century political contexts.
Despite their similarity in sound, dissemble and disassemble do not share roots. Assemble comes from the Old French verb assembler, which in turn has roots in the Latin assimulare, meaning to put together. Dissemble comes from the Old French dissembler, whose root sembler means to appear or to seem. So we can think of dissemble as meaning to dis-seem or to un-seem.
Dissemble is frequently used in place of disassemble—for example:
Near the end of the play the Grandmother dies on stage by dissembling herself — she removes her hearing aid, her false teeth, her eyeglasses, and her heart. [Huffington Post]
A bucket truck and forklift had to be brought in to dissemble the pyramid. [Fox 31 Denver]
Burglars dissemble a wall to break into SugarHill Studios. [CultureMap Houston]
But the word’s traditional sense is not dying; examples like these are just as easy to find:
[The films are] more ambitious than their American counterparts, revisiting painful moments from recent history and trying to drag suppressed or dissembled truths into the light. [New York Times]
[T]he word is that these are Chinese actors who have been hired to resemble and dissemble North Korean fans. [CBS News]
Francis Bacon seems noisy but dissembling, notoriously vague about both sources and process in his work. [Scotland on Sunday]
And for good measure, here are two examples of disassemble used well:
These fees cover the costs of recycling firms that disassemble the devices and sell the salvaged materials to commodities markets. [Guardian]
It will sell for about $18,500, disassembled, without windows or furniture. [New York Times]