what feature you want cut ?
This is just a trial not belongs to any problem.
I'll explain this easily for you.
"Geometric Condition" in this sense refers to a condition in which an invalid solid would occur if the command executed as intended. The geometric condition can also occur after the fact, meaning that the command executed properly but the result is a geometric condition that left the geometry unstable.
To understand the fully, you need to understand the definition of a solid and how the topology of a solid is used to mathematically determine if the solid is in fact a solid and not "open" or invalid. An invalid solid could be one where one or more of the surfaces of the solid intersect one another or when there is a "sliver" surface whose angle is less than the geometry tolerance.
A B-Rep (Boundary Representation) solid (virtually all software use B-Reps now), can be proven to be topologically correct if its elements are appropriately connected (e.g., all edges are connected to two vertices and bounded by two faces) and it adheres to an equation known as Euler's formula (derived by the 18th. century Swiss mathematician Leonhard Euler).
V - E + F = 2
V = # of vertices (points)
E = # of edges
F = number of faces
For example, this formula can be easily verified with a simple solid cube.
V = 8
E = 12
S = 6
8 - 12 + 6 = 2
This simple formula must be true after every command is competed. If not, then a "geometric condition" has caused it to be not true. An example could be one vertices miss-matched over another (outside the geometry tolerance) where a corner now has two points instead of one. This is just one condition. There are many more.
Now, there can be a geometric condition even if the formula is true. For example if one face of the cube is stretched into the cube and it intersects the opposite face. All vertices, edges and faces are the correct # but an interference is calculated.
This topology relationship between vertices, edges and faces is the root cause of why solids require more CPU time than wireframe or surface modelling. Every time you intersect a solid with any other curve, face or solid, the CAD system must determine the resulting topology is correct and the resulting solid is valid.
This is also why there are so many recommended best practices for working with solids, to minimize CPU time and more importantly to minimize the complexity of the topology of the solid so that error prone geometric conditions do not occur.
If you keep all this very simple stuff in mind it'll never happen again.............
Now I'll just wait for the comments......
Though your explanation is giving new perspective about the problem, I am thinking how to use your explanation to make clear this problem.
If you were to keep your model as is, but to trim the ends of the surface with a flat surface and knit the 3 surfaces together, would the cut with surface work any better in this condition w/o changing your model or modeling intent? Or when knitting the 3 surfaces, make it a solid and combine/subtract the volume.
..so, this is what happens when you retire and travel?
Maha,.. ..you can run a Tools/Check and find or look for the usual suspects.. in the spline (I think it is a spline?).. any sharp corners.. something which may fold onto itself or leave a sliver?