Probably not, although it is hard to always find reliable numbers, especially for sword duels prior to the 19th century, which is the period where they were considerably more deadly. If we look to the 19th century, where dueling with swords was still common in several countries including France and Italy, we have excellent statistical accounting thanks to several intrepid chroniclers of the period, but deaths were exceedingly rare, in the realm of 1 percent, and I can't think off hand of any in which both participants were killed.

If we go back further in time, sword duels were considerably more fatal, but we're now faced with the new problem of a shaky historical record. The reign of Henri IV in France, for instance, is reputed to have thousands of duelists die, but the range of estimates goes anywhere from 4,000 to 10,000, and as much of it is based on pardons granted to the survivor, almost by definition not everyone died. We are also faced with the conundrum that duels where no one died are the ones least reported, so while in his study of English duels Shoemaker finds 1/5 of duelists with swords were killed, and 1/4 wounded, but as he acknowledges, this is almost certainly an over representation as it is duels where someone died or was several injured that records are most likely, in this case based on a survey of several sources, including newspapers, and several famous collections of correspondence and diaries.

But one man dying is not the same as both, and although many accounts have mentioned of a single death, very few mention both. In part this likely relates to the incomplete record, and also the imbalance of wounds. Take for instance this account of a duel in 1772:

Young Sheridan and Capt. Mathews of this town, who lately had a ren­contre in a tavern inLondon, upon account of the Maid of Bath, Miss Linley, have had another this morning upon Kingsdown, about four miles hence. Sheridan is much wounded but whether mortally or not is yet unknown. Both their swords breaking upon the first lunge, they threw each other down and with broken pieces hacked at each other rolling upon the ground, the seconds standing by quiet spectators.

Did Sheridan die? Who knows, unless you can find another piece of evidence from later on, which is far too often lacking. Much of the record of duels prior to the 19th century is similar in nature, with mention of injury and uncertainty, and a lack of closure, so a duel with one dead and another helped from the field may very well mean the second man died of his wounds, yet we'll never know. There are some notable examples of this though, and while they don't quite give us the means to create a quantitative analysis, they are nevertheless interesting and worth mentioning! (Sheridan did survive, by the way)

It should be noted too though that duels of the early modern period were often not solitary affairs, with seconds standing by to observe, but rather everyone involved would participate. The principals would cross blades, and the seconds would too, and sometimes additional friends as well, as long as it was even on both sides. The result would sometimes be duels with multiple fatalities from both sides.

Initially developing in France, this vogue was present in England too for a time, and one duel that I can think of where the case was the death of both principles was that between the Duke of Hamilton and Baron Mohun in 1712. Accounts on the specific vary, but the end result was than both the principles ended up dead. According to the Duke's cousin and second, James Hamilton, the Duke had struck down Mohun with a fatal blow, but was himself somewhat injured, and Macartney, Mohun's second, having wounded Col. Hamilton as well then rushed over and killed the Duke who was unable to defend himself. The political stakes in the duel however cast a murky cloud over the entire affair, as this account was used as fuel to assert that the Duke had been assassinated, the duel carefully orchestrated by the Whigs to ensure his death, Mohun unable to accomplish it so then left to Macartney, who had orchestrated the whole affair, to finish. As such, it is an account that is treated delicately, and much more credence is given to the more straight forward account provided by the groom present, who described the Duke skewering Mohun, but himself receiving a cut to the arm that opened up an artery, and passing away within a few minutes from blood loss.

Another duel with multiple deaths that is worth mentioning was that in 1668 between the Earl of Shrewsbury and the Duke of Buckingham, although in this case of the principles, only Shrewsbury was felled in the affair. Both men showed up at the field with two seconds, for a three versus three engagement, and the account left to us by Samuel Pepys notes that everyone involved was wounded to some degree, with the Earl killed, and one of his seconds, Sir John Talbot, seriously wounded, while on the Duke's side a second named only as Jenkins was killed as well. The duel is also well remembered for the additional footnote that the Earl's wife, over whom the duel was fought, allegedly watched the duel dressed in disguise as a page... holding the Duke of Buckingham's horse. That part is likely mere rumormongering, but it was hardly unexpected given the Duke soon after kicked out his wife and began to live openly with the mistress he had just widowed...

So there are several examples, but I would again caution that they don't quite reflect a trend, and I'd also note too that the decline of the sword duel was in large part driven by the unequal contest that it created, and the perception that the winner of such a duel was too often predetermined. Not to say that duelists of equal skill did not face off, or that a lessor swordsman couldn't get in a lucky blow, but it is to say that the general view of duels was that both men dying was far from likely, outside of a true contest of equals. An anonymous Army captain, writing a guide for duelists in the late 18th century noted this as he commented favorably on the transition to the pistol as the dueling weapon of choice, since while a balanced contest could mean to very injured men, it was also a great rarity:

Every swordsman knows how rarely the parties are of equal skill, and if it should be so, what a number of wounds may be received on both sides, before the conflict is ended. Every surgeon also knows the ugly consequences of all such wounds, their extremities being often so deep and small as hardly to be come at.

There is debate as to whether the pistol duel made it safer, as different methodologies have resulted in different calculations of fatalities and injury (I take the side that it did reduce fatalities, but that is neither here nor there), but there is no debate that it made the contest more equal, with a number of rules and norms arising that intended to reduce the impact of skill as much as possible, and certainly the end result was more duels in which both participants were more liable to be jointly injured.

Sources

I maintain an extensive bibliography from which I am drawing for this answer.

[Also, if you want to learn more about dueling, I have a whole catalog of older answers.

Edit: Fixing up some gramer and spelnig