There is a plpgsql function is this post that splits a Line using multiple points.
However, it can also be done in a query, using generate_series, ST_Line_Locate_Point and ST_GeometryN to get knife points and ST_Line_Substring to split the line. Whichever you prefer, I leave up to you, as this query is not exactly terse.
CREATE TABLE sometable AS
lines as (SELECT ST_GeomFromText('LINESTRING(0 0, 2 2, 10 10, 15 15, 20 20)') as geom),
points as (SELECT ST_GeomFromText('MultiPoint((0 0), (2 2), (10 10), (15 15), (20 20))') as geom),
numgeoms (pt_count) as (SELECT st_numgeometries(geom) + 1 as pt_count FROM points),
knife_points as (
SELECT x as segment, CASE WHEN x = 0 then 0
WHEN x = (select pt_count from numgeoms) THEN 1 ELSE
ST_Line_Locate_Point(l.geom, ST_GeometryN(p.geom,x)) END as line_fraction_end,
CASE WHEN x = 1 THEN 0 else
ST_Line_Locate_Point(l.geom, ST_GeometryN(p.geom,x-1)) END as line_fraction_start
FROM points p, lines l, (SELECT generate_series(0, (SELECT pt_count from numgeoms)) as x ) g),
(SELECT ST_Line_Substring(geom, line_fraction_start, line_fraction_end) as geom, segment
FROM knife_points, lines WHERE segment >0 )
SELECT geom, segment from segments
WHERE ST_GeometryType(geom) = 'ST_LineString';
where you would replace the initial lines and points tables with your own. I suspect this query could be simplified quite a bit by using lead or lag, to get calculate each successive pair of knife points, but it does work.
The output of the above is,
LINESTRING(0 0,2 2) | 2
LINESTRING(2 2,10 10) | 3
LINESTRING(10 10,15 15) | 4
LINESTRING(15 15,20 20) | 5