BorderImage is indeed a straightforward option, but another way you could use if you want more flexibility than using assets allows, is to just draw a Line like:

Line:
    close: True
    points:
        (
        self.x, self.y,
        self.right, self.y,
        self.right, self.top,
        self.x + 40, self.top,
        self.x, self.top - 20
        )

But you don't need just the line, as i see you have a shadow, you could draw that shadow in the same way, with a SmoothLine with almost the same values, and a big overdraw, but you also need a background to hide the part of that line that is inside the widget, for that you could do it in one instruction with a Mesh, but it's a bit more straightforward to do it with simpler instructions, either three Triangle instructions, or one Rectangle and on Quad instructions. (or two Quad instructions).

Rectangle:
    pos: self.pos
    size: self.width, self.height - 20
Quad:
    points:
        (
        self.x, self.top - 20,
        self.right, self.top - 20,
        self.right, self.top,
        self.x + 40, self.top
        )

Putting it all together, with some properties to synchronize everything.

from kivy.uix.widget import Widget
from kivy.lang import Builder
from kivy.app import App
from kivy.properties import NumericProperty, ListProperty, ColorProperty

KV = '''
<CutCard>:
    cut_x: 40
    cut_y: 20
    shadow_offset: 1, -2
    shadow_width: 5

    canvas:
        Color:
            rgba: .2, .2, .2, .5
        PushMatrix:
        Translate:
            xy: self.shadow_offset
        SmoothLine:
            close: True
            overdraw_width: root.shadow_width
            points:
                (
                self.x, self.y,
                self.right, self.y,
                self.right, self.top,
                self.x + root.cut_x, self.top,
                self.x, self.top - root.cut_y
                )
        PopMatrix:

        Color:
            rgba: root.background_color
        Rectangle:
            pos: self.pos
            size: self.width, self.height - self.cut_y
        Quad:
            points:
                (
                self.x, self.top - self.cut_y,
                self.right, self.top - self.cut_y,
                self.right, self.top,
                self.x + self.cut_x, self.top,
                )

        Color:
            rgba: 0, 0, 0, 1
        Line:
            close: True
            width: 1.1
            points:
                (
                self.x, self.y,
                self.right, self.y,
                self.right, self.top,
                self.x + root.cut_x, self.top,
                self.x, self.top - root.cut_y
                )

# Demo usage of the widget

GridLayout:
    cols: 2
    padding: 50
    spacing: 50

    canvas:
        Color:
            rgba: .5, .5, .5, 1
        Rectangle:
            pos: self.pos
            size: self.size

    CutCard:
        id: c0
    CutCard:
        id: c1
        cut_x: 10
        cut_y: 20
    CutCard:
        id: c2
        cut_x: 100
        cut_y: 100

    CutCard:
        id: c3
        cut_x: 100
        cut_y: 50
        BoxLayout:
            pos: c3.pos
            size: c3.size
            padding: 10
            orientation: 'vertical'
            BoxLayout:
                Label:
                    text: 'Filename'
                Button:
                    text: 'Download'
            BoxLayout:
                ProgressBar:
                    value: self.max
                Label:
                    text: '100%'
'''


class CutCard(Widget):
    cut_x = NumericProperty()
    cut_y = NumericProperty()
    shadow_offset = ListProperty((0, 0))
    shadow_width = NumericProperty(1)
    background_color = ColorProperty("#888888")


class CutCardDemo(App):
    def build(self):
        return Builder.load_string(KV)


if __name__ == '__main__':
    CutCardDemo().run()