So basically you just want to cut away the threshold?
I am going to assume that the 4 x 1 is fixed to the 4 x2 upright studs, as how else would the frame work? I'm also assuming that it is stood on a concrete floor (is it?). Were I installing it I would probably have drilled the sole plate just beyond the doorway studs, then plugged and screwed the frame in place. Have you checked whether or not this has been done? (might require a torch and a mirror)
In the (probably unlikely) event that the sole plate is not adequately fixed down, take the door(s) off to start with. Drill two small horizontal pilot holes in the upright studs, one each side, 5 to 10mm deep, about 50 to 60mm up from the floor. Use these pilot holes as starter points for a larger drill bit (5 to 6mm - auger bit, brad point twist bit, or the like - not a Forstner bit, and I'd not recommend a spade bit, either) and drill your two 30° angled holes. Redrill the 5_6mm holes with a 7mm masonry bit, extending them about 50mm into the sub floor (are you sure there is no central.heating under there or a water pipe?). Push a brown plug in each hole, then push each gently down, tapping with a hammer until you only have 30mm or so of the screw (5.0 x 100 or 6.0 x 100mm) left sticking out. Tighten with an impact driver or combi drill until.the heads are sunk under the surface. Cut away the threshold with a multitool or a fine saw (bearing in mind that the blade will potentially get wrecked). Fill the screw head holes with 2 pack filler. Once set sand off with a power sander and reinstate the doors
An easier alternative might be to bracket the back.of the frame to the floor on the inside of the cupboard with a pair of 90 x 90mm angle brackets ficed to the floor and the studs before cutting out the threshold