They weren't to make battleships into minesweepers, but an attempt at self-protection, such that ship could sail through mined waters with at least some protection.
The paravane wires would have been fitted with cutters (mechanical or explosive). The idea was to divert the mooring wire (and hence mine) and then to cut or explode the mine. The paravanes would normally be streamed from the base of the bow, either via wires or a special fitting.
The drag of the wires/paravanes reduced speed.
As far as I know no battleship employed any acoustic sweep or electric sweep, although once invented all had degaussing coils.