Unselect after making a cut in Davinci Resolve 15
Assuming you work in the edit window, I guess you're using following:

press B to select Blade cut tool
mouse click on clip where you want to cut it
press A to switch to select mode
select cutted part I want to delete
press Delete

You can achieve something similar with Trim tool:

press T to select Blade cut tool
mouse click on clip where you want to cut it
press Shift+[ to Trim start (from left)
or Trim End with Shift+] (from right side)

This will make the clip shorter and if you click on the clip you'll see that it continues (the white box) only some part is shown:

now you can move which part of the clip is shown by pressing &lt; or &gt; (comma and dot keys)