I was a able to get the same functionality (i.e., mimicking Sublime Text's 'cut selection' functionality) by doing the following:
- Added the 'macros' extension by geddski:

- Added the following entries to my settings.json file (ctrl+shift+p, "Preferences: Open Settings (JSON)")
"macros": {
"cutLines": [
"expandLineSelection",
"editor.action.clipboardCutAction"
]
}
- Added the following to my settings json file (ctrl+shift+p, "Preferences: Open Keyboard Shortcuts"):
{
"key": "ctrl+x",
"command": "macros.cutLines",
"when": "!editorHasSelection"
},
To get VS Code to recognize the command I had to add uninstall and reinstall the "macros" extension. I presume adding the entries and then installing it for the first time would produce the same result.
For debugging purposes, here is a screenshot of my keybindings for "Ctrl+x" when I had everything working the way I wanted. Compare yours by typing "Open Keyboard Shortcuts" into the command prompt and searching for "Ctrl+x".
