tf.stop_gradient provides a way to not compute gradient with respect to some variables during back-propagation.
For example, in the code below, we have three variables, w1, w2, w3 and input x. The loss is square((x1.dot(w1) - x.dot(w2 * w3))). We want to minimize this loss wrt to w1 but want to keep w2 and w3 fixed. To achieve this we can just put tf.stop_gradient(tf.matmul(x, w2*w3)).
In the figure below, I plotted how w1, w2, and w3 from their initial values as the function of training iterations. It can be seen that w2 and w3 remain fixed while w1 changes until it becomes equal to w2 * w3.
An image showing that w1 only learns but not w2 and w3:
import tensorflow as tf
import numpy as np
w1 = tf.get_variable("w1", shape=[5, 1], initializer=tf.truncated_normal_initializer())
w2 = tf.get_variable("w2", shape=[5, 1], initializer=tf.truncated_normal_initializer())
w3 = tf.get_variable("w3", shape=[5, 1], initializer=tf.truncated_normal_initializer())
x = tf.placeholder(tf.float32, shape=[None, 5], name="x")
a1 = tf.matmul(x, w1)
a2 = tf.matmul(x, w2*w3)
a2 = tf.stop_gradient(a2)
loss = tf.reduce_mean(tf.square(a1 - a2))
optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.1)
gradients = optimizer.compute_gradients(loss)
train_op = optimizer.apply_gradients(gradients)