What you want is a sound board. I suppose you could find one that will work like your diagram but most likely it will have a different configuration. The way I would set it up is use the microphone as one input and the mixer as a second input and attach them to a mixer as inputs 1 and 2 respectively. From the mixer it connects to an amplifier and from the amplifier to the speakers. If either the mixer or speakers are powered then you can omit the amp stage.
The sound board can be a stand alone board or some other device like a phone, tablet or laptop.
If you insist on using that configuration you could have a microphone with a 3.5mm male connector plugged into the microphone input on your laptop. You can probably fine software to let you run samples and effects on the microphone input. Then you connect a 3.5mm male connector cable to your mixer/amp/speakers.
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