Most of these features don't work as you describe, but you could still get 120 ft out of Vicious Mockery with metamagic
Specifically, spell sniper cannot apply to Vicious Mockery because you don't make an attack roll:
You have learned techniques to enhance your attacks with certain kinds of spells, gaining the following benefits:
- When you cast a spell that requires you to make an attack roll, the
spell's range is doubled.
- Your ranged spell attacks ignore half cover
and three-quarters cover. You learn one cantrip that requires an
attack roll. Choose the cantrip from the bard, cleric, druid,
sorcerer, warlock, or wizard spell list. Your spellcasting ability for
this cantrip depends on the spell list you chose from: Charisma for
bard, sorcerer, and warlock; Wisdom for cleric or druid; or
Intelligence for wizard.
There's also no way to combine two spells. Both are actions and there's no mechanic to combine the spells even when cast the same turn. Even using metamagic to quicken one of them, they can't interact and affect each other.
You can still get 120 ft out of Vicious Mockery by using distant spell to double the range, but you cannot combine that with other metamagic options.
Vicious Mockery, then moving and hiding may be a better option
Either by using quicken spell metamagic + the hide action or multiclassing into rogue to get a cunning action to hide may give the effect you want, just with a little more hit and run.
Blink may also give you a similar effect you want
Assuming you always roll an 11 or higher for blink, you will always end up on the Ethereal Plane and out of direct combat. The effect of this will be you blink into existence long enough to insult a target then disappear before anyone knows what happens.
