New Spells: the Wizard's Armory (D&D 5e)

Shadowblade

illusion cantrip
Casting time: 1 action
Range: Self
Components: V, S
Duration: Instant

If a foe is distracted you can cause them to believe in an entirely phantasmal dagger you create. You make a melee attack and, if successful, the target suffers d4 psychic damage. Distracted targets are those that grant you advantage or have another enemy which is not incapacitated within 5 feet so long as you do not suffer disadvantage. 

If you wield an actual dagger you can use it as an anchor for your illusion, bolstering its power over their mind. You can either choose to use the attack above without the requirement that the target be distracted or you can cause an additional 1d6 psychic damage. This damage increases by 1d6 at 5th level (2d6), 11th level (3d6), and 17th level (4d6).

Baleful Teleport

conjuration cantrip

Casting time: 1 action
Range: 30 feet
Components: V, S, M (any small object or objects; usually stones, sticks, or even dirt taken from the ground)
Duration: instant
You cast an object towards a creature you can see within range and use your magic to teleport their matter into intersection. The creature must succeed on a Dexterity saving throw or take 1d10 force damage. This spell’s damage increases by 1d10 when you reach 5th level (2d10), 11th level (3d10), and 17th level (4d10).

Dismissal

Abjuration cantrip

Casting time: 1 action
Range: 10 feet
Components: V, S,
Duration: instant
You extend your hand toward a creature you can see within range and cause the very space about them to reject them, attempting to send them back whence they came. The creature must succeed on a Wisdom saving throw or take 1d4 force damage. 

Aberrations, celestials, elementals, fae, fiends, and undead suffer disadvantage on their save and the damage die is increased from d6 to d12. 

This spell’s damage increases by 1d6 (or 1d12) when you reach 5th level (2d6/2d12), 11th level (3d6/3d12), and 17th level (4d6/4d12).

Wind of Change

Transmutation cantrip
Casting Time: 1 action
Components: V, S
Range: 60 feet
Duration: Concentration, up to 1 round

You unleash a surge of riotous, transformative energy without focus or purpose and it takes hold as it will. This energy occupies a 5-foot cube centered on a point within range. In this area reality runs riot with uncontrolled metamorphosis, swords turn to snakes and arrows to butterflies before changing back again, individuals in the area find pieces of themselves converted to things from the animal, vegetable, and mineral kingdoms. The result is that attacks which originate, end, or cross through the area effected suffer disadvantage. Those who begin their turn in or moves into the area must immediately make a Constitution saving throw or suffer 1d4 damage as the random transformations cause them to injure themselves. If they suffer damage from this spell they must make a Wisdom saving throw or be stunned.

The spells damage increases by 1d4 and the maximum size of the cube's face increases by 5' at 5th (2d4, 10' cube), 11th (3d4, 15' cube), and 17th level (4d4, 20' cube).

Mindspike
Enchantment cantrip
Casting Time: 1 action
Components: V, S
Range: 60 feet
Duration: Instant
Your magic overwhelms the target's mind for a moment. The target must succeed on a Wisdom saving throw or take 1d8 psychic damage and be stunned.
The spell’s damage increases by 1d8 when you reach 5th level (2d8), 11th level (3d8), and 17th level (4d8).

Poor Aurum's Loom
divination cantrip
Casting Time: 1 action
Components: V, S
Range: 120 feet
Duration: Instant/special
The caster peers a few moments into the future and sees a moment primed for manipulation. By plucking this strand of fate they create an effect seemingly far out of proportion with the effort used.
Nothing happens on the round this spell is cast. At the end of their next turn they may choose their targets. The caster must then detail what unannounced action(s) they took during the previous round and how these snowballed to create an attack or attacks against the targets. No part of this description can change outcomes during the previous turn, though it may provide an alternative explanation for successes and failures, particularly those which were statistically unlikely, or other random occurrences. While the described occurrences may stretch the bounds of probability or reason but cannot create substantial changes to the environment, outright break the laws of physics, or have lack some intermediate step between the caster and target. If the player cannot provide some narrative for how this attack builds and manifests the cantrip fails outright.
The final result takes the form of an attack from the environment or an unattended object. This attack deals 2d4 damage. Before rolling the damage may be divided between one or more targets, but each target must risk one or more dice of damage. The type of damage is dependent on the feature used to make the attack against that target, and may differ between targets so long as the explanation justifies it. Each target may make a Wisdom save to notice the threat and adjust out of the way, negating this damage.
A wizard with the divination school arcane tradition is more proficient in divining the future broadly and not needing to be tangled with individual threads. As a result, these characters deny their targets the benefit from abilities like magic resistance and magic immunity.
The damage dealt increases by 2d4 at 5th level (4d4), 11th level (6d4), and 17th level (8d4).

~~*~~

I'm firmly in the camp that attack spells are, largely, wasted energy for wizards who should have far more interesting things to do. On the other hand, the vast majority of attack spells are simple "I throw energy at it" evocations. Especially as, for the moment, we seem to have mostly gotten away from the "I create stuff at it" conjurations, especially where the stuff is, y'know, energy-like (looking at you Orb of Force). So, I thought as an exercise I'd contemplate what a "direct damage" spell from the other schools might look like. My dream is that a specialist who wants to be a specialist  should be able to fill their allowed cantrips with specialty-school selections and, even if they aren't broadly functional, they will still be content with the abilities gained. (Conversely, there should be at least one "generalist" arcane tradition, though I've yet to get any ideas on that front.) I did exempt Necromancy from the exercise, as Chill Touch is a direct damage effect and pretty square with the general Necromantic vibe. There are a few amusing inspirations here, such as Numenera's Iron Winds showing up, but I'm particularly enamoured with the enforced storytelling of my Rube Goldberg device... Want damage? Sing for me so we can figure out the kind.