“Thou shalt not take the name of the Lord thy God in vain; for the Lord will not hold him guiltless that taketh his name in vain.” (Ex. 20:7.) So no swearing in the name of the Lord, or in other words, no using the Lord's name (or title for that matter) as a swear.
“But now ye also put off all these; anger, wrath, malice, blasphemy, filthy communication out of your mouth.” (Col. 3:8. Italics added) Often swear words are a means to communicate an emphases of emotion. One can be mad, or one can be mad as ****. The latter sounds stronger. Or, she could be mean, or she could be...well, the point is that these words are often used to make something have more impact as it were. Also, such words are often used as a means to offend or hurt someone. Could such a thing be acceptable to God? If we take the Apostle's words as if the Lord himself was speaking (which is how it is, see D&C 21:5 see also Titus 1:3), then we are disobeying God's commands, and thus, we offend God.
We, as saints and disciples of God, try our best to obey his words. Therefore, can a Mormon swear? Nope. I mean, anyone can technically swear as in they have the physical ability to; I mean, it's kinda easy, it's just a small handful of words; but Mormons cannot in good conscious use such language. And, if God's commands apply to all, then, technically speaking, no one should be using such language.
