If I understand your OP correctly, then you ask for using the scissor functionality to perform clipping as needed in a GUI's (often so-called) ScrollView? Although it is possible, going that way is not necessarily sufficient. Using scissor test is fine to cut off the last outlying pixels, but it is not suitable to cut off large portions. For the same reason one implements view culling in 3D.
Imagine an OutlineView or TableView. The table has 1000 lines of content from which 30 are shown inside the scroll area on screen. Rendering 970 invisible lines is obviously a waste of performance. Instead, having some kind of view culling here would be of great benefit. Or imagine a view where a nodal graph is displayed at a more or less high zoom level. Again, doing some view culling before rendering would be beneficial.
To restrict the actual rendering (keyword clipping) you can use at least these techniques, some of them based on a 3D API (IIRC you are using OpenGL, aren't you?):
a.) Using the scissor test. This allows for axis-aligned, rectangular, and pixel based clipping.
b.) Using the stencil test. This allows for arbitrary pixel based clipping if you are able to generate the stencil mask accordingly.
c.) Using discard in the pixel / fragment shader alternatively to stencil.
d.) Using an opacity mask and blending. Sometimes one can see that the head and/or foot areas in a TableView are faded out, just as indicator for "here follows more".
e.) Using RTT and crafted mapping geometry. This allows for more or less arbitrary edges and holes.
BTW: A ScrollView does not necessarily need a ScrollBar. Grabbing the scrollable view and shifting it around is common. Graph visualization software as well as 2D graphics editors allow this since the dawn of time, but nowadays it is pushed by mobile apps and has found its way into other desktop applications. However, that doesn't unburden you from clipping.