Tłumaczenie z oxforda może to coś rozjaśni.


mutter /'mt(r)/
I. n mamrotanie n
II. vt wy|mamrotać [prayer, reply]; mru|knąć, -czeć pod nosem [curse, insult]; 'too bad,' he muttered "niedobrze", mruknął; (imitating people conferring) 'mutter , mutter' "gadu-gadu" infml
III. vi mamrotać, mruczeć; to mutter about doing sth przebąkiwać o zrobieniu czegoś; to mutter to oneself mamrotać do siebie; what are you muttering about? infml co ty tam mruczysz?



mumble /'mmbl/
I. n mamrotanie n
II. vt wy|mamrotać [apology, reply]; 'sorry,' he mumbled "przepraszam", wymamrotał
III. vi to mumble to oneself mamrotać do siebie



murmur /'mm(r)/
I. n
1. (of traffic) szum m (of sth czegoś); (of voices, stream) szmer m (of sth czegoś)
2. (expressing reaction) szmer m, pomruk m; a murmur of disapproval/agreement pomruk or szmer dezaprobaty/głosy poparcia; to obey without a murmur usłuchać bez szemrania
II. vt wy|szeptać [words, thanks]; to murmur sth to sb szepnąć coś komuś
III. vi
1. (make gentle sound) [person] mruczeć, szemrać; [stream] szemrać; [wind] szumieć
2. (complain) szemra

Witaj Dex92- sporo napisane w wolnej encyklopedii, zobacz,

MUTTER,
http://www.thefreedictionary.com/mutter
MURMUR
http://www.thefreedictionary.com/murmur
MUMBLE,
http://www.thefreedictionary.com/mumble

Pozdrawiam- jkp

W jaki sposób chciałbyś by ktoś to napisał własnymi słowami?
Wyraźnie widać, że są to synonimy i różnica między nimi jest minimalna.
Różnią się natomiast zakresem stosowalności co widać po przykładach ze słownika podane wcześniej przez DoRi_OlGaAA.

Nie będę oryginalny ale zerknij na to:
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murmur noun
1 sound of words that are spoken quietly

adjective
dull , faint , low , quiet , slight , soft
general
a general ~ of assent
angry , excited

verb + murmur
give , let out
He gave a little ~ of relief.
hear

murmur + verb
ripple through sth , run
A ~ of excitement rippled through the audience.
A ~ of amusement ran around the room.

preposition
in a   ~
She answered in a low ~.
with a   ~
He took the mug of coffee with a ~ of thanks.
without a   ~
They did as they were told, without a ~.
~   of

phrases
the ~ of voices
2 low, gentle, continuous sound

adjective
soft
low
distant

verb + murmur
hear

preposition
~   of
the distant ~ of traffic
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mumble verb

adverb
incoherently
quietly , softly
quickly
sleepily
angrily , bitterly
sarcastically

preposition
about
I couldn't understand what he was mumbling about.
into
She ~d something into her pillow.
to
George ~d incoherently to himself.

Mumble is used with these nouns as the object: apology , excuse , reply , word
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mutter verb

adverb
gruffly , harshly , hoarsely
through clenched teeth , through gritted teeth
‘I don't need a drink,’ she ~ed through clenched teeth.
aloud
loudly
quietly , softly , under your breath
silently
sleepily
incoherently , vaguely , weakly
angrily , bitterly , crossly , darkly , fiercely , furiously , grimly , irritably , sourly , sullenly
Helen began ~ing darkly about hospitals.
miserably , sadly
nervously
sheepishly
drily , sarcastically

verb + mutter
be heard to , hear sb
A number of visitors were heard to ~ that it would not have happened at home.
She heard him ~ an oath under his breath.

preposition
about
She ~ed something about the incompetence of the office staff.
to
He was ~ing incoherently to himself.

Mutter is used with these nouns as the object: apology , curse , obscenity , prayer , reply , swear word , word
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Oxford Collocations Dictionary for Students of English, 2nd edition

PS. Jak będę miał czas to poddam edycji te informacje by były bardziej przejrzyste.
Uważam, że nauka w ten sposób, "dictionary crawling", że to tak ujmę może często udzielić odpowiedzi na takie pytania.
Robiąc to samemu zyskuje się sporo, przyda się też kilka dobrych słowników.
Co do synonimów przydatny jest słownik kolokacji, bo na jego podstawie widać kiedy i w jaki sposób dane słowo jest używane.

Pozdrawiam

za ODE
mutter - 1 say something in a low or barely audible voice, especially in dissatisfaction or irritation:
[with object] :
he muttered something under his breath
[with direct speech] :
‘I knew she was a troublemaker,’ Rebecca muttered
2 [no object] talk or grumble in secret or in private:
back-benchers were muttering about the next reshuffle

mumble - 1 [reporting verb] say something indistinctly and quietly, making it difficult for others to hear:
[with object] :
he mumbled something she didn’t catch
[with direct speech] :
‘Sorry,’ she mumbled
2 [with object] bite or chew (something) with toothless gums or without making much use of the teeth:
she mumbled a piece of black bread

murmur - 1 [reporting verb] say something in a low or indistinct voice:
[with object] :
Nina murmured an excuse and hurried away
[with direct speech] :
‘How interesting,’ he murmured quietly
[no object] (murmur against) archaic express one’s discontent about (someone or something) in a subdued manner:
now they do not simply murmur against him, they quarrel noisily with him
2 [no object] make a low continuous sound:
the wind was murmuring through the trees


W rozwiewaniu podobnych wątpliwości pomaga mi ten słownik
http://www.pearson.pl/angielski/katalog-sklep/slowniki-angielsko-angielskie-dla-zaawansowanych/longman-language-activator.html
Jest dość dogi ale warto. Można go czytać do poduszki:-)