I have used fondant on several occassions on top of a thin layer of buttercream icing. However, upon cutting the cake, the fondant is rather difficult to cut through. Can anyone tell me what I am doing wrong?

How long after applying the fondant are you cutting it? The longer it is on a cake the more chance it will dry out some.
Maybe you need a slightly thicker coating of b'cream?

Are you covering the cake or is it open to the air? I find that when I forget to cover the cake with plastic wrap or some type of covering the fondant gets hard and does not taste as good. Also what recipe or brand are you using for your fondant, because that could also be the problem?

HTH!

Fondant is always going to be more difficult to cut through than buttercream. Use a really sharp serrated knife and start your cut with a slight sawing motion rather than just pushing down. Usually, it's just the surface of the fondant that dries and underneath that, it's nice and soft, and so is the cake.

What Karensue said, plus be sure to clean off the blade after every slice. I have used a non-serrated sharp blade with success, too, with the "sawing motion" start.

I have been using Wilton fondant. The first and last cake that I used it on was a wedding cake that I covered with buttercream icing. Perhaps the buttercream was not thick as mention in a reply. However, the cake was covered in fondant the next day and left in open air until the wedding later that afternoon, about 6 hours.