The whole sentence is taken from the film Quadrophenia and it's uttered by a judge in a trial: "These long-haired, mentally unstable, sawdust Caesars" referring to the mods who went to Brighton during the Mod vs. Rockers English era and were involved in violence and disturbances down there.
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The quote is indeed used in Quadrophenia, however its use in that film was taken from a genuine court case where the judge used the same phrase (interestingly, many of the references in that courtroom scene was taken from genuine court cases involving 'Mods and Rockers' in that period, such as the "will you take a cheque" quote). The Stanley Cohen book "Folk Devils and Moral Panics" is a great study of the real historical background to Quadrophenia.
Anyway, the phrase "Sawdust Caesar" seems to come from a reference to Mussolini - initially Mussolini was seen as the new Caesar by many Italians but after Italy's capitulation he was seen as a "Sawdust Caesar" - emperor of only the chipboard maps used to plan troop movements.
However, the term seems to have been used for Mussolini even earlier - a George Seldes book published in 1935 was named "Sawdust Caesar: the Untold History of Mussolini and Fascism"
It means that they are heroes not for longtime.
Sawdust is something definitely not lasting, like soldiers who died heroically in a battle, they were heroes few seconds, and then they died unfortunately.
From some Google searches, I've learned it seems to mean that he's a poor imitation of a Caesar. He is not made out of solid wood but, rather, pressed together out of sawdust. He's a cheap imitation. It's figurative, of course.
So it's similar to "paper tiger" (a calque from the Chinese).
Children's dolls used to be made of leather or fabric, stuffed with sawdust. I think that would be the kind of Caesar meant: a stuffed doll of a Caesar, or as kentix says, "a poor imitation" of one.
Edit: In Italy Mussolini was even represented as a puppet conqueror:
In the Dopolavoros, children's puppet shows depicted Mussolini and Italian troops strewing the stage with battle corpses of blackpainted “African bandits and barbarians." Twentieth-Century Caesar: Benito Mussolini
(The "Dopolavoros" were Fascist after-work recreation centres.)