Kreasound has some remix competitions in various styles
Metapop site has several remix competitions running
Splice has some remix competitions
Remixcomps.io lists various competitions
Tips
Some tips on how to win a remix contest
Useful Tutorials
This video describes how to detect the tempo of a track. This will be very useful for making the bars and beats line up with the audio files that we will use for our remix. The first 6 mins of this video describe how to do it very well. It might take you a few attempts to get used to the process. Remember this link is here and you can rewatch the video whenever you start a new remix.
Cardijn Tips for Remix 1