try{

        Class.forName("com.mysql.jdbc.Driver").newInstance();
        Connection conn = DriverManager.getConnection(
                "jdbc:mysql://localhost/internacionalizacija?useUnicode=true&characterEncoding=UTF-8", "root", "");

        String sql = "INSERT INTO utakmice(tim1, tim2, datum) VALUES(?,?,?)";
        PreparedStatement stmt = conn.prepareStatement(sql);
        //stmt.execute("set names 'utf8'");

        stmt.setString(1, utakmice.getTim1());
        stmt.setString(2, utakmice.getTim2());
        stmt.setDate(3, utakmice.getDatum());

public class Games {
    private String tim1;
    private String tim2;
    private DateFormat datum;

    public Utakmice(String tim1, String tim2, DateFormat datum) {
        this.tim1 = tim1;
        this.tim2 = tim2;
        this.datum = datum;
    }


    public void setTim1(String tim1) {
        this.tim1 = tim1;
    }

    public String getTim1() {
        return tim1;
    }

    public void setTim2(String tim2) {
        this.tim2 = tim2;
    }

    public String getTim2() {
        return tim2;
    }

    public void setDatum(DateFormat datum) {
        this.datum = datum;
    }

    public DateFormat getDatum() {
        return datum;
    }
}

private void btnSpremiActionPerformed(java.awt.event.ActionEvent evt) {

    String tim1 = txtTim1.getText();
    String tim2 = txtTim2.getText();
    DateFormat datum = txtDate.getDateFormat();

    Utakmice utakmice = controll.kreirajUtakmice(tim1, tim2, datum);
    controll.spremiUtakmice(utakmice);
}

public Calendar getSelectedDate() {
    return chooser.getSelectedDate();
}

Date datum = txtDate.getSelectedDate().getTime(); //Might be null if nothing selected !!

public class Games{
    private String tim1;
    private String tim2;
    private Date datum; //CHANGED HERE

    //getter and setter
}

SimpleDateFormat sdf = new SimpleDateFormat("yyyy-MM-dd");
//Convert a String into a Date (matching the pattern above
Date d = sdf.parse("2017-09-20");
//Convert a Date into a String(matching the pattern above
String s = sdf.format(d);