Select an option from the Curve Editor tab > Edit panel > Segment menu to cut or merge curves:
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Cut — Click to break a curve either, at a user-defined point or, into a specified number of equal-sized curves. For closed curves, the first cut point is always at the original start point (point 1), subsequent cut points depend on the options you choose. Click Curve Tools tab > Points panel > Select to determine the start point.
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Split — Select to break the selected segments into the individual curves used to create it. If no segments are selected, then, all segments are split.
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Merge — Click to merge individual selected segments into one curve. Select the segments you want to merge then click Curve Editor tab > Edit panel > Segment > Merge to merge them. Self-intersecting sections are not merged.
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Automatic Merge — Click to merge all the segments adjacent to the picked segment.
Click Curve Editor tab > Edit panel > Segment > Automatic Merge and then select a segment. The curve editor automatically searches for segments that join the picked segment, at either end, and merges them. The search then starts again on this new segment, to see if any segments join it. If they do, then they are merged. This continues until no more merges are possible. Where there is a choice of curves to merge, the curve with the smallest tangent angle discrepancy is chosen. Hold the Alt key while clicking on a segment to automatically merge it.