Is a compound simply a mixture of two or more elements?

No. A mixture of elements would just be a mixture. The components of the mixture would remain chemically distinct. In a compound the elements are chemically bound to one another and behave as a single substance with its own set of properties.

As an example, water (H2O) is a compound of hydrogen and oxygen that is liquid at room temperature. If you simply mix together hydrogen and oxygen, all you have is a mixture of gasses that will explode if exposed to a spark. This reaction will produce water vapor.