I am told (by Allan) that TextMate currently doesn't support a kill buffer such as used with yank. Instead is has a built in clipboard-history with hotkeys from moving back and forth etc.
Alternatively, do the following to record a macro which mirrors kill:
Automation -> Start Macro Recording, cmd-shift-arrow right, cmd-x, Automation -> Stop Macro Recording, Automation -> Save Scratch Macro... as ctrl k.
In the future, a kill buffer may be implemented, also to allow macros to not disturb the clipboard.