Let's assume we have the following layers "borders" (line) and "ocean" (polygon), see image below.

With the following geoalgorithm Vector > Geoprocessing Tools > Difference..., it is possible to delete edges of the polygons that border the ocean.

The output new "borders" layer will look as following

Keep on mind that this object is a MULTILINESTRING.

In case, it should be treated as a simple LINESTRING, please proceed with Vector > Geometry Tools -> Multipart to singleparts. There is a useful subject on this topic, see Convert MultiLineString to LineString using QGIS

Let's assume there are two layers 'borders' (line) and 'ocean' (polygon), see image below.

With the "Difference" geoalgorithm can be found under Vector > Geoprocessing Tools > Difference, it is possible to delete edges of the polygons that border the ocean.

The output new 'borders' layer will look as following

Keep on mind that this object is a MULTILINESTRING.

In case, these features should be treated as a simple LINESTRING, please proceed with "Multipart to singleparts" can be found under Vector > Geometry Tools > Multipart to singleparts. 

There is a useful subject on this topic, see Convert MultiLineString to LineString using QGIS

Let's assume we have the following layers "borders" and "ocean", see image below.

With the following geoalgorithm Vector > Geoprocessing Tools > Difference..., it is possible to delete edges of the polygons that border the ocean.

The output new "borders" layer will look as following

Keep on mind that this object is a MULTILINESTRING.

In case, it should be treated as a simple LINESTRING, please proceed with Vector > Geometry Tools -> Multipart to singleparts. There is a useful subject on this topic, see Convert MultiLineString to LineString using QGIS

Let's assume we have the following layers "borders" (line) and "ocean" (polygon), see image below.

With the following geoalgorithm Vector > Geoprocessing Tools > Difference..., it is possible to delete edges of the polygons that border the ocean.

The output new "borders" layer will look as following

Keep on mind that this object is a MULTILINESTRING.

In case, it should be treated as a simple LINESTRING, please proceed with Vector > Geometry Tools -> Multipart to singleparts. There is a useful subject on this topic, see Convert MultiLineString to LineString using QGIS