The ratio of the horizontal to the vertical component of the vector is proportional to the ratio of the horizontal and vertical difference in position. The proportion factor is the speed divide by the direct distance (calculated by the pythagorean theorem).
distance.x = target.x - start.x;
distance.y = target.y - start.y;
distance_direct = square_root((distance.x * distance.x) + (distance.y * distance.y)); // pythagoras
vector.x = distance.x * (speed / distance_direct);
vector.y = distance.y * (speed / distance_direct);
Note that this will result in a division by zero when the distance is zero (start and target position are identical). That makes sense, because in that case the vector is undefined (in what direction do you not-go when you want to stay where you are?). This case needs to be handled separately.
Note that there is no reason to use degree here. When you have an angle in degree and a speed, you can convert it to x and y direction using sine and cosine:
vector.x = sin(angle) * speed
vector.y = cos(angle) * speed
In most programming languages, the sine and cosine functions use radiants, not degrees. That means a full 360° circle is 2*PI (approximately 6.283185) you can convert degree to radiants by multiplying them with
PI / 180 or approximately 0.01745329.