It doesn't look like the circuit makes a return and everything seems to be parallel so it should be fine.
WRONG ADVICE
Don't do it.
There are 3 channels for RGB - and there are 3 LEDs in series (one in each package) for each channel. Each channel has a single resistor for current limiting - 150 ohm, 150 ohm and 330 ohm. I'll bet you the 330 ohm resistor is on the red channel.
Cut where you have shown and you won't get ANYthing lighting up in that section. This is
why they have the cut points clearly marked.
You could trace out the appropriate paths and work out the proper resistor values to have just that section with one LED package light up - but I have an alternate suggestion for you....