How to create foreign key that is also a primary key in MySQL?

Add FOREIGN KEY (sale_id) REFERENCES Sale(sale_id) to each foreign table:

CREATE TABLE Sale(
    sale_id CHAR(40),
    PRIMARY KEY(sale_id),
    discount DOUBLE,
    type VARCHAR(255),
    price DOUBLE
) ENGINE=INNODB;

CREATE TABLE Normal_Sale(
    sale_id CHAR(40),
    PRIMARY KEY(sale_id),
    FOREIGN KEY (sale_id) REFERENCES Sale(sale_id)
) ENGINE=INNODB;

CREATE TABLE Special_Sale(
    sale_id CHAR(40),
    PRIMARY KEY(sale_id),
    FOREIGN KEY (sale_id) REFERENCES Sale(sale_id)
) ENGINE=INNODB;

Just make sure your database is InnoDB which supports Foreign References.