The words do, dew, due sound the same but have different meanings and spellings. Why do do, dew, due sound the same even though they are completely different words?
The answer is simple: do, dew, due are homophones of the English language.
Water droplets condensed from the air, usually at night, onto cool surfaces.
Something moist, fresh, pure, or renewing: "The timely dew of sleep/. . . inclines/Our eye-lids” ( John Milton).
Moisture, as in the form of tears or perspiration, that appears in small drops.
To wet with or as if with dew.
To perform or execute: do one's assigned task; do a series of business deals.
To fulfill the requirements of: did my duty at all times.
To carry out; commit: a crime that had been done on purpose.
To produce, especially by creative effort: do a play on Broadway.
Payable immediately or on demand.
Owed as a debt; owing: the amount still due.
In accord with right, convention, or courtesy; appropriate: due esteem; all due respect.
Meeting special requirements; sufficient: We have due cause to honor them.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.