The short answer
Mark Twain did use it, and said he was quoting someone else. In an instalment of his autobiography published in the North American Review on 5 July 1907, he wrote: “Figures often beguile me, particularly when I have the arranging of them myself; in which case the remark attributed to Disraeli would often apply with justice and force: ‘There are three kinds of lies: lies, damned lies, and statistics.’” So the line is genuinely in Twain, but it is not genuinely his, and Twain himself did not claim it.
Not Disraeli either
Benjamin Disraeli died in 1881. Quote Investigator found the remark first credited to him in a letter to The Times and The Standard in July 1895, which said “Lord Beaconsfield” (Disraeli's title) had spoken of “three degrees of veracity—viz., lies d—d lies, and statistics.” No one has found it in Disraeli's own speeches or writings.
A joke that grew
The saying grew in steps. In the 1880s lawyers and judges were quoted joking that witnesses came in three classes, ending with “experts”. In 1891 versions appeared with statistics in third place: “a fib, a lie, and statistics”. In 1892 the politician Arthur Balfour was reported using “lies, damned lies, and statistics”. Quote Investigator concludes that the saying cannot be credited to a single creator.