Dragging a slider is sometimes not precise enough for how you want to clip things. If you wanted more precise control over the start and end times for your clip time range, then you can use the timestamp controls in the bottom right of the clipping window:
The first textbox holds the clip start timestamp and the second textbox holds the clip end timestamp. You can modify the timestamp manually by typing in a valid timestamp value (HOURS:MINUTES:SECONDS). Clicking the timestamp sync button () next to each textbox will use the clipping window's current video timestamp as the start or end timestamp.