This article applies to Studio 16 & Avid Studio.
If there is a Speed effect applied to a clip in Stretch mode and you split that clip, the clip will split into two identical copies with the speed effect applied to both. This is because Stretch mode always strives to keep the same frame both at the head and tail of the clip. This works in your favor when trimming a clip a little longer or shorter with the intent to keep the same material on the timeline. However, when you split a clip, essentially you have made a second head and a second tail, both striving to keep the same head and tail frames.
To avoid these issues, it is best to split the clip before adding any speed effect. Once you have the clip(s) that way you want them, and then apply any effects.
If you want to trim out a section of the middle of the clip and already have a speed effect applied, it is best to remove the speed effect first and then split the clip. You can then edit it however you want and then re-apply the speed effect.