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Let's say I have a QuantumCircuit with depth $d$ layers. How can I generate a new QuantumCircuit with the last n layers removed. For example, let's say the QuantumCircuit has $d=8$ layers as follows:

Quantum Circuit with Depth 8 Layers

And let's say the last n=4 layers are desired to be removed then the resulting QuantumCircuit should be as follows leaving only the first 4 layers of the above QuantumCircuit:

Removed Last 4 Layers from QC

How can this be done in Qiskit?

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Please notice that the previous answer may unnecessarily remove gates. It depends on the order you insert them in your circuit.

For example, constructing the circuit you provided with the following code

qc = QuantumCircuit(2)

qc.sdg(0)
qc.h(0)

qc.y(1)
qc.h(1)
qc.s(1)

qc.cx(0, 1)
qc.cx(1, 0)

qc.h(0)
qc.s(0)
qc.h(0)

qc.h(1)
qc.s(1)
qc.h(1)

print(qc)
---
     ┌─────┐┌───┐          ┌───┐┌───┐┌───┐┌───┐
q_0: ┤ SDG ├┤ H ├───────■──┤ X ├┤ H ├┤ S ├┤ H ├
     └┬───┬┘├───┤┌───┐┌─┴─┐└─┬─┘├───┤├───┤├───┤
q_1: ─┤ Y ├─┤ H ├┤ S ├┤ X ├──■──┤ H ├┤ S ├┤ H ├
      └───┘ └───┘└───┘└───┘     └───┘└───┘└───┘

and after removing the last 2 layers with your method we get

     ┌─────┐┌───┐          ┌───┐┌───┐
q_0: ┤ SDG ├┤ H ├───────■──┤ X ├┤ H ├
     └┬───┬┘├───┤┌───┐┌─┴─┐└─┬─┘└───┘
q_1: ─┤ Y ├─┤ H ├┤ S ├┤ X ├──■───────
      └───┘ └───┘└───┘└───┘          

Notice how the last 3 gates acting on qubit 1 disappear although we should keep one extra Hadamard.

For a more robust solution, we should work with a representation of the circuit that captures the topological dependencies present, i.e DAGCircuit.

from qiskit.converters import circuit_to_dag, dag_to_circuit

dag = circuit_to_dag(qc)
layers = list(dag.multigraph_layers())

n_remove = 2

# the extra minus 1 since the last layer consists of output nodes (qubits and clbits).
for layer in layers[- n_remove - 1:]:

    for node in layer:
        if node.type == 'op':
            dag.remove_op_node(node)
                   
new_qc = dag_to_circuit(dag)

print(new_qc)
---
     ┌─────┐┌───┐          ┌───┐┌───┐
q_0: ┤ SDG ├┤ H ├───────■──┤ X ├┤ H ├
     └┬───┬┘├───┤┌───┐┌─┴─┐└─┬─┘├───┤
q_1: ─┤ Y ├─┤ H ├┤ S ├┤ X ├──■──┤ H ├
      └───┘ └───┘└───┘└───┘     └───┘
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Based on this question I have been able to solve this problem as follows:

initial_d = qc.depth() # in my case 8
n = 4 # number of layers to remove
while qc.depth() > (initial_depth - n):
    qc.data.pop(-1)
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