As far as I know, there isn't a way to remove all Transitions at once, which is strange considering there's an easy way to remove all Effects (right-click clip selection > Remove Effects...)
I believe a FR is in order for this, to add Video Transitions/Audio Transitions checkboxes to the dialogue box and rename it to 'Remove Effects/Transitions...' I've never needed to remove a bunch of transitions from a sequence but that doesn't mean this added functionality couldn't help others who need to do this.
The next version of PP is almost here, so perhaps this has already been added. I'll wait and see. If it's not there I'll add a FR for this and suggest you do to: https://www.adobe.com/cfusion/mmform/index.cfm?name=wishform