Nice slash animation there dude.
And I second the recommendation of that book. It's hella cheap on Amazon, and for what and how it teaches you, I've not seen or heard of anything that tops it yet.
Also echoing what wolfenoctis mentioned, as far as animation in pixel art goes, it's definitely good practice to keep your animations rough until you've nailed the movement you're after.
It's difficult to realize this as a beginner to both pixel art and animation, since, if you're anything like I was when I got started, you'll probably be thinking "well, the more I can copy/paste in an animation, the less work I'll have to do later since most of the pixel-work is already done," which is faulty logic when it comes to animation where small expressive sprites are required (such as the case is with yours) because a single pixel in the wrong place can ruin the form you're trying to express, and this is double-true when that tiny set of pixels need to express subtle movement over multiple frames (since there is no concept of sub-pixel movement when it comes to animations in small sprites -- so you'll have to use other colors/shades to blur the pixel between two locations, or leave that pixel where it is until the correct moment when the movement is significant enough to allow it to translate to a new position).
As mentioned/shown already, it is better to redraw the image in flat colors if your sprite is small (and only copy/paste static chunks with slight tweaks to simulate perspective shifts when the sprite is large, redrawing everything else in flat colors that connects the chunks together) because this gives you the ability to change subtleties in the essence of your movement + expression (even at very small scales such as this one), and that stuff does matter very much. You should put in as much -- or more -- thought and work into planning your movement as you do into your pixel-placement.
If you play with it long enough, you'll find that animation can be just as fun, perhaps even moreso, than drawing/designing the character itself. This sense of enjoyment only comes when you realize that animation is not just something you have to do for your game, but what actually gives your characters and worlds their life, and this can be changed easily by simply tweaking a motion where you might think a character *should* go up, and making him go down instead. The more you play with it, the more you do your own thing with your movements, the more you'll both learn and enjoy it. Though, whatever you do, remember that you've got to keep a sense of weight and follow-through in your motions (even the impossible ones), or they'll be dull and lifeless.
Motion is simply the translation of mass and energy from one point to another, usually in the form of an arc.
In the slashing animation you have here, figure out the main arc of the slash, and make the head/body/shoulder/arm/elbow/hand follow it in succession. What you do with the *rest* of the body is what gives your slash the 'expression' wolfenoctis was referring to.
In the case of what I was describing to you earlier, that's a standard kendo/samurai style slash, but your character doesn't need to be a master japanese swordsman if that's simply not in his character. He could slash just like you would swing a bat, and as long as the body moved convincingly enough (i.e. it expressed sufficient anticipation, action, & recovery to compensate for the entire motion), it would be an effective animation, no matter what way you decided to move the body or sword during the attack.