Let's assume that you want to remove overlapping lines in QGIS:
Vector > Geoprocessing Tools > Symmetrical difference
If there are several geometries in both layers, you might get an error when using the previous tool. In such cases, I recommend creating a buffer of a few meters for each line.
Vectorial > Geoprocessing Tools > Buffer with fixed distance
Now, use the symmetrical difference tool again, and you'll get something like the following:
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