Truly, it's hard to analyze anyone's golf game without being able to see a swing.  However, the slice is so universal to about 80% of golfers that it's worth spending some time on how to deal with it.

I posted a video with a drill that has helped a lot of my students.  The most likely cause of the slice is yanking the club at the top of the backswing hard "over the top", which just means that you're pulling the club down towards the ball to HIT it, instead of swinging the club through the ball.   It's perfectly natural- in most ball and racket sports, you have to make a hard move to hit at the ball, as in tennis or baseball.  However, golf isn't that kind of sport- the ball will sit there forever waiting for you, and by really trying to go agressively through the ball, people pull the club with their left side and end up slashing across the ball, creating the left to right spin that creates that hard slice.  So what to do?  Yes, try the drill. The drill is intended to make you drop the club likely much more behind you than you're used to, and feel how hitting the inside portion of the ball can feel. But again, without being able to see your individual swing it could be a number of factors that are the root cause of your slice. 

One way to guarantee to create a slice is by aiming to adjust for one.  By aiming further left, you actually open your body to the target and create even more of an opportunity (and likelihood) that you'll hit even further across the ball, and slice it worse.  Believe me, I know you're just trying to get the ball go where it's supposed to, and for a short time while you're working on getting rid of a hard slice, play with the swing you have.  However, the best way to work on eliminating a slice is to try to hook the ball instead.  First, definitely do this on the driving range before taking it to the course (and put away the driver at first- do this with a 6 or 7iron).  Pick a target- a flag, or maybe the 150 sign, or even a house or tree in the distance.  It doesn't matter, as long as it's clear- we need something to judge the results of your efforts clearly.  Second, take a club out and step behind the hitting area.  Line that club up on the ground so that you can aim your feet about 10-15 yards RIGHT of your intended target.  As I mentioned above, if aiming left can help promote a slice, aiming right can help promote a hook or draw.  Step up to the ball (and doing this after the above drill is a solid idea to feel how not to pull the club over the top) and align your feet to the club you just set on the ground 15 yards right of your target.  Now look up at the target and keep that picture of the target in your mind as you swing the club.  Sometimes it can be helpful for golfers to think about swinging along your foot alignment or along the clubline.  Ideally, this will break the paradigm of aiming left and hitting across the ball.  Don't expect the first ball to be a perfect tight draw.  However, if you continue to align yourself along the club you've set down, try to turn the ball over and create some right to left spin on the ball.  A famous teacher, Harvey Penick, described it as aiming at right field and trying to hit a hooking line drive over the shortstop.  Sometimes it's necessary to feel like the whole left forearm or arm is turning left, almost like turning the wheel on a steering wheel, but I'd prefer if you don't have to think about rotating your arms while you swing.  Believe me, you're going to feel awkward enough changing your alignment already.  Just keep swinging down that clubline and trying to bring that ball back to the target.  And be nice to yourself- whatever you've been doing to slice the ball, you've been doing it for a looooong time.  Don't expect it to be completely fixed in a few swings.  As long as you're seeing the ball starting to the right of the target, even if you're not yet able to get it all the way to draw yet, you'll be able to get it there eventually.

I hope that helps.  I'll be checking in with the blog regularly, so let me know how it goes in the comments section.  I'll definitely answer any questions you might have- this can be complicated to describe in words.