Did Mark intend to depict Jesus as a carpenter? The answer appears obviously yes as Mark 6:3 reads in most translations:
3 Is not this the carpenter, the son of Mary, the brother of James, and Joses, and of Juda, and Simon? and are not his sisters here with us? And they were offended at him.
However nothing is as simple as they seem. First note how the author of Matthew sourcing Mark phrases the passage, 13:55 :
55 Is not this the carpenter's son? is not his mother called Mary? and his brethren, James, and Joses, and Simon, and Judas? 56 And his sisters, are they not all with us? Whence then hath this man all these things? 57 And they were offended in him.
The usual explanation for the difference is that by the time Matthew wrote his version the idea that Jesus was a lowly carpenter had become offensive and an embarrassment and so Matt modified it a bit to lessen the damage to Christianity's image. Personally I think this is silly. Matthew in other places freely alters or ommits whole stories in Mark. If the author had felt that calling Jesus a carpenter was an embarrament why retain the word at all? Why not just say something like , "Is this not Jesus? is not his mother....". It seems little different as far as image goes whether a would be king was a carpenter or had come from a lowly carpenter's family.
Now this discussion could go in many different directions such as why would the writer of Mark or his sources mention that Jesus family was not wealthy, or specifically why call him a carpenter of carpenter's son? For those who believe that the story is literal history the explanation is simple, he was a carpenter and carpenter's son, that's why Mark and Matt wrote it down. Even most "historical Jesus" scholars usually assume the author would not have included this detail unless it was true because of the potential embarrassment it would create. Those of the "Jesus Myth" camp however wonder the thematic value of depicting Jesus as a comon man chosen to become the Messiah ( or receiving the Christ if doceticsm is included). Heros often came from the ranks of the working class so this detail in Mark in itself may not have been an obstical to attracting lower class folks to the new religion but rather the opposite. Also it has been noted here before how Homer's works influenced most all literature of the day and Mark is no exception. Interestingly Odysseus is described as a "master carpenter" and the possibility should not be ruled out that Mark or a redactor described his Jesus as a carpenter for reasons of emmulating this influential work.
However, (I seem to use that word alot) I am of the mind that the writer of Mark did not describe Jesus as a 'carpenter' but rather a 'son of a carpenter' just like Matt.
First as I said above I find the argument that Matt deliberately altered Mark here unconvincing. If Matt did not, then obviously the copy of Mark he had read as Matt does today, ie.'son of carpenter'. So I view Matt's reading as evidence that his copy of Mark originally read, "son of carpenter'.
Secondly, IMO the text reads better as Matt has it than Mark. Matt has the crowd listing the family of Jesus, Father, Mother , brothers, sisters, in an orderly and logical way, while Mark seems oddly constructed. Jesus is first described as a carpenter then his family minus a father is listed. The absence of any reference to a father in Mark has spawned theological speculation that Joseph was dead by this point in the story, something quite at odds with Matthew where the crowds speak of Joseph as living.
Thirdly, the manuscript evidence is nearly split on the reading. Rather than bore everyone with lists of manuscripts suffice it to say that 3rd century ms and a number of 4-5th cent. mss read Mark just like Matthew ie. 'son of carpenter'. Yet also a number of 4th-5th mss have Mark say Jesus was a carpenter. Scholars like Metzger and Aland prefer the reading as it appears in most translations, explaining that it was a question of plausibilty. They, just as argued about Matt above, see the alledged emmendation of Mark as a result of Christianity's embarrassment about worshipping a carpenter. If however that logic is flawed or unpersuasive the question still remains which way Mark read originally. There are a few ancient manuscripts whose copyists chose to avoid the issue by simply ommitting the carpenter reference altogether, much like I suggested Matt would have done if he had found it offfensive.
Fourth, Origen writing around 180 pointly said in contra Celsum : "In none of the Gospels current in the churches is Jesus himself ever described as a carpenter." This means he had not seen Mark 6:3 as it reads today. Was it changed before that? Was he and the churches not using Mark because of the verse in question? We may never know.
5th, It would make a great deal of theological sense to change the text of Mark from "son of carpenter' to "carpenter'. There are a number of such recognized alterations that specifically sought to remove references to Jesus father as fossils from a time before the virgin birth doctrine was fully established. See: The Orthodox Corrruption of Scripture.
It really should be mentioned that the word translated 'carpenter' in these verses is tekton meaning a broad range of construction and craftsman related activities. In the LXX for example the word is used of workers with iron and bronze. So broad is the meaning that some commentators have suggested the word be understood as simply 'blue collar', and indictative of social class rather than specific trade. It really is only tradition that associated Jesus or Joseph with wood working.
So at the end of this rambling I must say, I prefer the conclusion that Mark originally did not say Jesus was a carpenter but that this was either a scribal error of perhaps the result of someone emmending the verse just a touch to better align with Homer's description of Odysseus or more likely making one less reference to Jesus having been fathered.