Spellblade

This deck is essentially a modified, somewhat lower-power version of the tournament winning lists by @Maubuss and @Flickstar, with some other ideas from other various tournament lists such as those by @Assorted Animals (Anthony) and @Count Tolstoy.

Here we're aiming to keep a lot of the very low-to-the-ground and aggressive play patterns while also cutting out a lot of the more powerful (and more expensive) pieces, and instead replacing them with different cards that fill a similar role in the deck. Speaking of, there are really 3 main pillars to any Battlemage deck that we need to keep in mind while building: acceleration, mobility, and survivability.

Mobility

If we're going to be punching people in the face, we need to not spend forever running around the board.

Mobility is one of the key pillars to a successful Battlemage. Cards like Whirling Blades, Blink, Grapple Shot, Blaze, and Flanking Maneuver are all pretty key here. However, there are also a few minion-based mobility options as well, such as War Horse and Siege Giant that work pretty well for what we need.

Survivability

Since we're so heavily incentivized to attack with our avatar, we're going to be taking a lot of damage, and we need to keep away from death's door as well as we reasonably can.

Daperyll Vampire or alternatively Vampire Bats can be used to regain a bit of life since we'll be throwing ours in the woodchipper.

The Manor at Daperyll Hill gives us a bit of removal that doesn't cost us mana or spells while also giving us a bit of extra lifegain.

Rhongomyniad is mostly here to be carried, and not thrown, as it'll allow us to strike first, allowing us to kill without being killed.

Grapple Strike, Whirling Blades, and similar allow us to strike enemies, allowing us to kill without being damaged. Notably though, getting a kill from a strike doesn't allow us to draw a card.

Flaming Sword in a similar vein, allows us to splash kill a bunch of minions when we attack, which will allow us to draw a card for each of them, which is fantastic.

Acceleration

This is unfortunately the category that really depends on some expensive staples. Since Battlemage wants to get moving and attacking as early as it can, that means alternative means of mana help quite a bit. The only true mana rock I'm utilizing in this version of the deck is Ruby Core, but others like Amethyst Core, Philosopher's Stone, Four Waters of Paradise, Key to the City, and Shrine of the Dragonlord are all also really beneficial for this.

Anti-Hate Cards

Feast for Crows can be used to strip cards like Toolbox, Sphere of Animosity, and Disencant/Dispel out of your enemies' decks.

Vindictive Nation helps us prevent, or at least punish, the disruption of our manabase.