We propose utilizing a polarization-tailored high-power laser pulse to extract and accelerate electrons from the edge of a solid foil target to produce isolated subfemtosecond electron bunches. The laser pulse consists of two orthogonally polarized components with a time delay comparable to the pulse duration, such that the polarization in the middle of the pulse rapidly rotates over 90° within few optical cycles. Three-dimensional particle-in-cell simulations show that when such a light pulse diffracts at the edge of a plasma foil, a series of isolated relativistic electron bunches are emitted into separated azimuthal angles determined by the varying polarization. In comparison with most other methods that require an ultrashort drive laser, we show the proposed scheme works well with typical multicycle (∼30 fs) pulses from high-power laser facilities. The generated electron bunches have typical durations of a few hundred attoseconds and charges of tens of picocoulombs.