The major difference between these verses and those in Matthew are the change from “it had been said” in Matthew to “it hath been written” in 3 Nephi. The “verily, verily” has been added to verse 32, but it doesn’t alter the meaning.
These verses are difficult for modern readers because we understand, and the Church allows, that there are times when divorce is appropriate. The intent of these verses is also likely to be an amplification of divorce conditions. In that context, Jesus is contrasting the ease of obtaining a divorce under the law of Moses with the desire to treat marriage as a serous contract. Jesus did note that there were conditions where divorce would be necessary, although the only one he listed was fornication. Even without a list of other conditions, the idea is that marriage is to be treated seriously, and not ended frivolously.
There is no way of knowing what the conditions surrounding divorce might have been in the New World. The teaching that it was to be treated seriously would still have been applicable.