Tuesday being pronounced chewsday illustrates one outcome of a process called
palatalization. The segment "tu" being pronounced /tju/; it's a short hop, skip, and jump to /tʃu/. This sort of thing happened a lot in Romance languages: Latin "c", pronounced /k/, becomes "ch", /ʃ/, in some environments in French. Think of how "c" is pronounced in Italian before "a", "o", and "u", differently than before "e", "i": /k/ ~ /tʃ/. Another example is how Latin
diurnus became French
jour and Italian
giorno: /dju/ => /dʒo/.
The US pronunciation of the "t" in Saturday is not actually a voiced alveolar stop /d/, but people hear it that way usually. It's rather an
alveolar tap: [ɾ]. The process is sometimes called
flapping. It is not a phoneme in English, but an allophone. It is the same as Spanish "r" intervocalically, as in
pero 'but'.
