With your MTB SPD pedals you will have a tension screw to adjust how hard the pedal holds the shoe. You should wind them right down so they release easy. Run them like this for a few rides and slowly turn up the tension.
The problem you are having is, without clips you are used to putting your inside foot down around corners. You need to re-learn how to ride and gain confidence in your equipment and skills to be able to corner at high speed without putting your foot down.
Hope this helps