How to pause, resume and stop pyttsx3 from speaking?

There is no pause and resume function provided by pyttsx3, but you can simulate these feature by splitting the sentence into words, and then speak word by word. In between words, you can check whether pause, unpause or stop button is clicked and do corresponding action:

from tkinter import *
import pyttsx3
import threading

root = Tk()

class Speaking(threading.Thread):
    def __init__(self, sentence, **kw):
        super().__init__(**kw)
        self.words = sentence.split()
        self.paused = False

    def run(self):
        self.running = True
        while self.words and self.running:
            if not self.paused:
                word = self.words.pop(0)
                print(word)
                engine.say(word)
                engine.runAndWait()
        print("finished")
        self.running = False

    def stop(self):
        self.running = False

    def pause(self):
        self.paused = True

    def resume(self):
        self.paused = False

speak = None

def read():
    global speak
    if speak is None or not speak.running:
        speak = Speaking(text.get(1.0, END), daemon=True)
        speak.start()

def stop():
    global speak
    if speak:
        speak.stop()
        speak = None

def pause():
    if speak:
        speak.pause()

def unpause():
    if speak:
        speak.resume()

engine = pyttsx3.init()

text = Text(width=65, height=20, font="consolas 14")
text.pack()

text.insert(END, "This is a text widget\n"*10)

read_button = Button(root, text="Read aloud", command=read)
read_button.pack(pady=20)

pause_button = Button(root, text="Pause", command=pause)
pause_button.pack()

unpause_button = Button(root, text="Unpause", command=unpause)
unpause_button.pack(pady=20)

stop_button = Button(root, text="Stop", command=stop)
stop_button.pack()

mainloop()

Update: Using pygame as the player:

from tkinter import *
import pyttsx3
import pygame

pygame.mixer.init()
engine = pyttsx3.init()

root = Tk()

def read():
    outfile = "temp.wav"
    engine.save_to_file(text.get('1.0', END), outfile)
    engine.runAndWait()
    pygame.mixer.music.load(outfile)
    pygame.mixer.music.play()

def stop():
    pygame.mixer.music.stop()

def pause():
    pygame.mixer.music.pause()

def unpause():
    pygame.mixer.music.unpause()


text = Text(width=65, height=20, font="consolas 14")
text.pack()

text.insert(END, "This is a text widget\n"*10)

read_button = Button(root, text="Read aloud", command=read)
read_button.pack(pady=20)

pause_button = Button(root, text="Pause", command=pause)
pause_button.pack()

unpause_button = Button(root, text="Unpause", command=unpause)
unpause_button.pack(pady=20)

stop_button = Button(root, text="Stop", command=stop)
stop_button.pack()

mainloop()