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On 6.8.beta4, i have a different behaviour, with no assumption:

sage: f(x, y, z) = sqrt(x^2 + (y+1-z)^2)
sage: f.taylor(x, 0, 3)
(x, y, z) |--> -1/2*x^2/(y - z + 1) - y + z - 1

Which version are you using ?

On 6.8.beta4, i have a different behaviour, behaviour (which might be seen as a regression), with no assumption:

sage: f(x, y, z) = sqrt(x^2 + (y+1-z)^2)
sage: f.taylor(x, 0, 3)
(x, y, z) |--> -1/2*x^2/(y - z + 1) - y + z - 1

Which version are you using ?

On 6.8.beta4, i have a different behaviour (which might be seen as a regression), the following behaviour, with no assumption:

sage: f(x, y, z) = sqrt(x^2 + (y+1-z)^2)
sage: f.taylor(x, 0, 3)
(x, y, z) |--> -1/2*x^2/(y - z + 1) - y + z - 1

Which version are you using ?This can be considered as a bug of too much simplifying.