Mirror image only affects attacks, and blight and magic missile aren't attacks.
Mirror Image (PHB p.260):
Three illusory duplicates of yourself appear in your space. Until the spell ends, the duplicates move with you and mimic your actions, shifting position so it’s impossible to track which image is real. You can use your action to dismiss the illusory duplicates.
Each time a creature targets you with an attack during the spell’s duration, roll a d20 to determine whether the attack instead targets one of your duplicates.
If you have three duplicates, you must roll a 6 or higher to change the attack’s target to a duplicate. With two duplicates, you must roll an 8 or higher. With one duplicate, you must roll an 11 or higher.
A duplicate’s AC equals 10 + your Dexterity modifier. If an attack hits a duplicate, the duplicate is destroyed. A duplicate can be destroyed only by an attack that hits it. It ignores all other damage and effects. The spell ends when all three duplicates are destroyed.
A creature is unaffected by this spell if it can’t see, if it relies on senses other than sight, such as blindsight, or if it can perceive illusions as false, as with truesight.
Attacks are only things that require an attack roll (weapon attacks and spell attacks). See P. 194 of the PHB:
If there’s ever any question whether something you’re doing counts as an attack, the rule is simple: if you’re making an attack roll, you’re making an attack.
("Attack" has a specific rules meaning in 5e that isn't the same as its ordinary English meaning; actions and spells that might be described as attacks in ordinary language aren't necessarily attacks as far as the 5e rules are concerned.)
If a spell doesn't say that the caster makes a spell attack, then mirror image doesn't interact with it. This is clear from the complete spell description above: the spell effects only occur if the caster is targeted with an attack, and its effects consist only of changing the target of the attack to one of the duplicates. The only way to determine if a duplicate is hit is by resolving the attack against the duplicate's AC. There is no provision for mirror image interacting with spells that (for example) require the target to make a saving throw.
It might be argued that the first paragraph, particularly the phrase it’s impossible to track which image is real, establishes that mirror image makes reliably targeting the caster with any effect impossible. There are other spells that interfere with the targeting of non-attack spells, and they spell out those effects specifically:
Nondetection (PHB p.263):
The target can’t be targeted by any divination magic ...
Antimagic field (PHB p.213):
Spells and other magical effects, such as magic missile and charm person, that target a creature or an object in the sphere have no effect on that target.
If mirror image affected the targeting of non-attack spells, we would expect there to be a specific clause in the description that spells that interaction out. For example, something beginning with "When a creature targets you with a non-attack spell ... ". But there is no such wording; the effects described apply only to attacks.
It might also be argued that mirror image clearly creates illusions which are valid targets for spells, so a hostile spellcaster might target one of these illusions by accident.
However, mirror image doesn't create illusions; it creates illusory duplicates, and it specifically spells out all of their effects. Spells that create illusions (such as major image or minor illusion) have different effects (and they don't specify what happens if they are targeted by a spell, attack or otherwise).
So, to consider the two spells in the question:
Blight (PHB p.219):
Necromantic energy washes over a creature of your choice that you can see within range, draining moisture and vitality from it. The target must make a Constitution saving throw.
Magic missile (PHB p.257):
You create three glowing darts of magical force. Each dart hits a creature of your choice that you can see within range.
Magic missile just hits the actual creature being affected by mirror image, and doesn't affect the images at all. It's not an attack, because no attack roll is made; it just does damage. Blight likewise ignores the images and affects the target, as it also is not an attack.
So there is no "trying" to target the caster, you simply target the caster and automatically hit them, as that is the creature you are targetting. (Illusions are not creatures.)
After that, Mirror Image actually does nothing, as per Does Mirror Image affect spells that have no attack roll?
So no, you can't use Magic Missile to get rid of Mirror Image duplicates.