Deleting a row section after you have built it is difficult. You can see that the string consists of one MATLAB object with the following code:
x = 1:10; y = 1:10; H = plot(x, y, '-o'); get(H, 'children')
ans =
Empty Matrix: 0-by-1
We see that the line has no children, so there is no βsub-partβ that we can remove. However, there are some cheeky tricks that we can use to try to achieve the same effect.
Separate two lines separately
... using hold on . See Victor Hugo's answer. This is the right way to achieve our goal.
Separate two separate lines in one
MATLAB does not dial points with a value of NaN. By modifying the input vectors, you can make MATLAB skip the point to give a dashed line effect:
x = [0 1 2 2 3 4 5 6 7 8 9]; y = [0 1 2 nan 3 4 5 6 7 8 9]; plot(x, y, '-o');
This is equivalent to plotting the line from [0, 0] to [2, 2], skipping the next point, then starting it again in [3, 3] and continuing [9, 9].

Erase part of a line
This is the nastiest way to do this, but it is a cheap hack that can work if you are not worried about changing your input arrays. First draw a line:
x = 1:10; y = 1:10; plot(x, y, '-o');

Now draw a white line over the part you want to erase:
hold on plot([2 3], [2 3], 'w');

As you can see, the result is not entirely correct and will respond poorly if you try to do other things on the chart. In short, I would not recommend this method, but it can come in handy in desperate times!