Somewhere in the archives of this listserv is my previous answer to this
very question, detailing some of the times Twain's voice was recorded (by
accident by an opera star, at a dinner, his dictations for THE AMERICAN
CLAIMANT, etc). It is reported that some survived but were destroyed in WW2
in Europe. Not sure which ones those might have been. But none are known to
have survived, and you can assume that I've looked in all the right places.
The actor whose imitation of Twain that Hal Holbrook refers to is William
Gillette's recording of a portion of the jumping frog story that he
performed in the 1920s. He gave performances imitating Twain as late as
1935. His first performance was during Twain's lifetime, and witnessed by
Twain, who pronounced it excellent. Clara Clemens likewise heard Holbrook
imitate her father and said he was a dead ringer, so...  we don't have the
old man himself, but we do have something pretty close.

Kevin Mac Donnell
Austin TX