The Collaborative International Dictionary of English v.0.48:

Mumble \Mum"ble\, v. t. [imp. & p. p. Mumbled; p. pr. & vb. n.
   Mumbling.] [OE. momelen; cf. D. mompelen, mommelen, G.
   mummelen, Sw. mumla, Dan. mumle. Cf. Mum, a., Mumm,
   Mump, v.]
   1. To speak with the lips partly closed, so as to render the
      sounds inarticulate and imperfect; to utter words in a
      grumbling indistinct manner, indicating discontent or
      displeasure; to mutter.
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            Peace, you mumbling fool.             --Shak.
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            A wrinkled hag, with age grown double,
            Picking dry sticks, and mumbling to herself.
                                                  --Otway.
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   2. To chew something gently with closed lips.
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