What is Mugen chewing?
Anime characters chewing on a blade of grass/toothpick is considered a trope in anime and is usually attributed to the delinquent types.


  Sometimes a character will suck or chew on something as a form of
  characterization. These range from toothpicks and blades of straw or
  grass to lollipops and cigarettes.
  
  In anime, having a piece of straw in one's mouth is a common depiction
  of a banchou, or juvenile delinquent gang-leader character.


Some other characters that have been noted to conform to this trope:


Tetsuya Kusakabe from  Katekyo Hitman Reborn!, a delinquent character.





Ikki Takeda from History's Strongest Disciple Kenichi, who was formerly a member of a gang called Ragnarök.





Mifune from Soul Eater, who's personality is described like this:

Often stoic in nature and staunch in attitude, Mifune tends be somewhat quiet in situations that do not directly involve him and remains mostly serious as well as being straight-forward..





Ash's Treecko from  Pokémon, described as cool, calm, collected and serious.






Wikia, on Mugen:
Rude, lewd, vulgar, conceited, temperamental, and unhinged - Mugen is something of an antihero.

Thus, it can be inferred that the "blade of grass in mouth" trope is a type of characterization that mostly represents a serious/delinquent sort of character. 



The plant isn't usually of significance and isn't the same in every case unless explicitly stated. In a Japanese page that describes Ikki Takeda from the second image above, the following is written with respect to the blade of grass. 


  常に葉っぱを口でくわえて...


which translates to "Always with a leaf in his mouth...", indicating that he's not chewing on any special plant.

As for what Mugen is chewing in the particular image posted, I'd guess it's bamboo.